Journey to Function Ridge An Algebraic Odyssey
BackStory
Start Game
Backstory: Enter Dr. Shaylee Owusu
Shaylee Owusu, a brilliant and daring mathematical archaeologist, has spent years studying ancient legends of the Elixir of Infinite Mathematical Knowledge. Hidden atop the perilous cliffs of Function Mountain lies the Apex Domain Shrine, a mysterious place said to grant ultimate understanding of numbers, functions, and equations to those who prove their mastery. Equipped with her climbing gear, sharp mind, and unwavering determination, Shaylee begins her ascent. At each checkpoint along the mountain, she must solve challenging function-based puzzles to continue her climb. Only by reaching the summit and completing the final series of trials at the Apex Domain Shrine can she claim the fabled elixir. Success will reward Shaylee with boundless mathematical insight, while failure risks the Shrine’s magical defenses — powerful energy currents that can sweep away even the most skilled adventurer. Shaylee’s journey is not just a climb of stone and snow, but a test of her intellect, courage, and perseverance. Will she conquer Function Mountain and unlock the secrets of the Apex Domain Shrine, or will the mountain’s challenges prove too great?
Next
Functions Tutorial
A function is basically a rule that connects numbers. You put one number in, the rule does something to it, and you get exactly one number out.
- The number you put in is called the INPUT or DOMAIN.
- The number you get out is called the OUTPUT or RANGE.
- The Domain is the x-value of an ordered pair
- The Range is the y-value of an ordered pair
Let's take a look at this table for example
(1,3) (2, 5) (3, 7)
See how each x-value has one y-value? That’s exactly what makes it a function.Every x-value listed on a table or a group of ordered pairs must have one x-value match with one y-value. If you see a number repeating in the x column, then its not a function. Click the next button to see an example of what I mean rookie adventurer.
Next
Look at how the table and the ordered pairs at the bottom have a repeating x-value. This is an example of something that is NOT A FUNCTION, because the x-value is linked to different values. IN A FUNCTION, X-VALUES SHOULD NEVER REPEAT!
(1,3) (2, 5) (3, 7) (1, 2)
Next
Let's Test What We've Learned!
Which of these two tables represents a function?
Ok, so the tables are great and all, but you're probably asking, "How exactly did you come up with the numbers for the table Shaylee?
Here’s the kicker: we didn’t just make them up. We used the function rule.
A function rule is just the instruction or formula that tells you how to get the output (y-value or Range) from the input (x-value or Domain).
A common example would be the Slope a of Line formula: y = mx + b
y is the y-value of a point on the line. m is the slope, which tells you how steep the line is. b is where the line crosses the y-axis.
y = mx + b is just a rule. It tells you, if you pick an x, how to get the y that goes with it. And that… my friends… is exactly what a function does.
Next
You know how a linear equation, such as, y =2x +3, has the letter y at the beginning. A function is the same way but instead of the letter y, we represent with something different Normally, a function is represented by the notation f(x) We can write this same idea in function notation, which looks like this: f(x) = 2x + 3 f(x) just means ‘the output when we put x into the function.’ So instead of saying y, we say f(x). It’s just another name for the output.
Next
For Example: If f(x) = 2x + 3 and x = 1, then f(1) = 2*1 + 3 = 5. That’s exactly the same as saying y = 5 if x = 1. There are lots of ways we can write functions: y = 2x + 3 f(x) = 2x + 3 Even g(t) = 2t + 3 (sometimes we use other letters instead of x)
Next
"Alright, let’s look back at our original table and figure out the function that made these numbers.
Step 1: Look at the x and y pairs. x = 1 → y = 2 x = 2 → y = 4 x = 3 → y = 6 Step 2: Ask yourself, ‘What did we do to x to get y?’ 1 → 2 (multiply by 2) 2 → 4 (multiply by 2) 3 → 6 (multiply by 2) Step 3: Write the rule. Multiply x by 2. In function notation, that’s: f(x) = 2x
Next
"Here’s another way to figure out the function rule, especially if the table looks tricky.
You can pick any two points from the table and find the slope between them. Then use that slope to write the equation.
Step 3: Use point-slope form to write the equation. Formula: y - y1 = m(x - x1) Plug in (1,2) and m = 2 → y - 2 = 2(x - 1) Step 4: Simplify to slope-intercept form. y - 2 = 2x - 2 → So the rule is f(x) = 2x
Step 1: Pick two points from the table.Let’s pick (1, 2) and (2, 4).
Step 2: Find the slope (m). Formula: m = (y2 - y1) / (x2 - x1) m = (4 - 2) / (2 - 1) = 2 / 1 = 2
Next
Let's Test What We've Learned!
"Okay, rookie, one more thing before we start climbing!
Sometimes you’ll be given the graph of a function, and your job could be any of these: Find the function rule – the equation that describes the line. Find f(x) – the output for a given input. Find x – the input that gives a specific output. The graph of a function f is shown. For what value of x is f(x) = 3?’
Click here for the answer
Let's Test What We've Learned!
Functions Tutorial
LET THE ADVENTURE BEGIN!
Next
Level One: Rocky Slope of Variables
"Click and drag Shaylee towards the dot, then click on the finger icon."
Answer this question to continue your journey.
Which of the following sets of points represents a function of x?
A) {(−1, 2), (0, 3), (1, 4)}
B) {(1, 2), (1, 3), (2, 4)}
C) {(-2,0), (0,0), (2,0), (0,1)}
Click here for Help
D) {(0,1), (1,1), (2,1), (3,1)}
Wrong Answer!
Let's Try Again
"Lucky for you I had the helicopter ready, or Shaylee would’ve been snake chow! Now, let’s take this one step at a time. A function is a rule that assigns exactly one output (y-value) to each input (x-value). This means if an x-value appears more than once with different y-values, that set cannot be a function. Let’s look at the options carefully: Option A: {(−1, 2), (0, 3), (1, 4)} — each x-value is unique, so it could be a function. Option B: {(1, 2), (1, 3), (2, 4)} — notice the x-value 1 appears twice with different y-values. That breaks the rule, so it is not a function. Option C: {(-2,0), (0,0), (2,0), (0,1)} — the x-value 0 repeats with two different outputs. This is also not a function. Option D: {(0,1), (1,1), (2,1), (3,1)} — each x-value is unique and maps to one y-value, so this is a function. Often, players focus only on the pattern of the y-values or think a function has to be a straight line — that’s a common mistake. The key is always to check the x-values first. Eliminate any sets where an x-value repeats with a different y-value, then verify the remaining options carefully. That’s how you determine which set represents a function."
Click here to Try Again
Level Two: Cliff of Linear Challenges
"Click and drag Shaylee towards the dot, then click on the finger icon."
Answer the question to continue your journey.
Click here to answer the qeustion
Let's Try Again
*"Luckily, I was climbing close by, right near Shaylee, just in case she got into trouble! Now, let’s carefully think about this question. A function is a rule that assigns exactly one output (y-value) to each input (x-value). That means for every x-value, there can only be one corresponding y-value — no repeats with different outputs. Now, let’s look at the options: A. Every input is paired with at least two outputs. Nope — functions only allow one output per input, so this is wrong. B. Every input has exactly one output. I have hunch this might be what we are looking for. C. Every output must pair with exactly one input. Close, but not required — multiple x-values can share the same y-value. D. The graph is always a straight line. Wrong — functions can be curves, parabolas, or other shapes; they don’t have to be straight lines. A common mistake is to think a function must be a straight line, or to focus on outputs instead of inputs. Always check each input to make sure it only has one output — that’s how you know it’s a function!"
WRONG ANSWER!
Click here to Try Again
Level Three: Boulder Pass of Patterns
"Click and drag Shaylee towards the dot, then click on the finger icon."
Answer the question to continue your journey.
Click here to answer the qeustion
Let's Try Again
We have to hurry before something monsterous eats Shaylee! Alright, let’s break this down carefully. We need to evaluate f(2) for f(x)=2x squared − 1. The key is to follow the order of operations carefully: exponents first, then multiplication, then subtraction. That’s step one — don’t rush it, or we could make a mistake while the carnivores are closing in. Now, let’s look at the options: Option A: 7 — if you properly square the 2 first, multiply by 2, and then subtract 1, this is a strong candidate. Option B: 3 — this might come from forgetting to square first or miscalculating the multiplication. Double-check the order of operations here. Option C: 8 — maybe someone multiplied before squaring, or skipped the subtraction at the end. Think carefully about which step is missing. Option D: 5 — this could happen if subtraction is done incorrectly or if a step in the formula is skipped. Here’s a hint: follow the operations in the right sequence — exponents → multiplication → subtraction. Eliminate the options that don’t follow the proper order, and you’ll narrow it down to the right choice without guessing. Stay focused — every second counts!"
WRONG ANSWER!
Click here to Try Again
Level Four:The Yeti Range
"Click and drag Shaylee towards the dot, then click on the finger icon."
Answer the question to continue your journey.
Click here to answer the qeustion
Let's Try Again
*"Lucky for you I was close by, or those snow yetis would’ve caught you! Let’s look at these points: (0,1), (1,2), (2,4), (3,8). Option A: Yes — linear. Think about whether the differences between outputs are consistent for each step in x. Option B: No — nonlinear. Could the changes in y suggest it’s not constant? Option C: Not a function. Remember, a function only allows one output per input. Option D: Yes — exponential only. Watch for patterns that grow by a factor rather than by equal steps. Check each option carefully, focusing on how the y-values change relative to x-values. That will guide you to the right choice."
Click here to Try Again
WRONG ANSWER
Level Five: Stormy Peak/ Summit Climb
"Click and drag Shaylee towards the dot, then click on the finger icon."
Answer the question to continue your journey.
Click here to answer the qeustion
Let's Try Again
Shaylee almost froze to death up there! Luckily, I was able to set up a base camp near her. Now, let’s take another look at the problem. Remember, the range or output refers to the y-values. Given the set of ordered pairs {(−1, 4), (0, 4), (1, 5)}, what is the range? Option (A) {−1, 0, 1} — This can’t be correct because it lists only the domain, or x-values. Option (B) {4, 5} — This looks promising because we see 4 in both (−1, 4) and (0, 4). Remember, y-values can repeat in a function. Option (C) {−1, 4, 1, 5, 0} — This choice just lists all the numbers we have without identifying which are domain or range. Option (D) {4} — This isn’t correct because there is more than one number in the range for this set of ordered pairs. Check each option carefully, focusing on how the y-values change in relation to the x-values. That will guide you to the correct choice.
Wrong Answer
Click here to Try Again
Click here to Try Again
Level Five: Stormy Peak/ Summit Climb
"Click and drag Shaylee towards the dot, then click on the finger icon."
"Dr. Shaylee Owusu… You have climbed the frozen heights and braved the shadows of slumbering beasts. Now, your final trial begins." "Before you rests the Elixir of Infinite Mathematical Knowledge — a gift bestowed only to those who prove both wisdom and resolve." "Answer ten questions of logic and number. You must succeed in at least six. Only with a score of sixty percent or higher shall the elixir be yours." "But heed this warning: should you fail… the mountain’s blessing shall become its burden, and a fate of confusion and frustration will shadow your path." "Prepare yourself, student of numbers. The test begins now."
Begin
Click her to begin the final challenge
What was your Final score?
D) 40%
G) 70%
A) 10%
B) 20%
H) 80%
E) 50%
F) 60%
I) 90%
C) 30%
J) 100%
Click here for text to speech
I) 100%
Congratulations!
Shaylee has the Elixir of Infinite Mathematical Knowledge!"
Exit
GAME OVER!
QUICK CLICK HERE!
QUICK CLICK HERE!
Saving D.r Shaylee
Functions Tutorial
A function is basically a rule that connects numbers. You put one number in, the rule does something to it, and you get exactly one number out.
- The number you put in is called the INPUT or DOMAIN.
- The number you get out is called the OUTPUT or RANGE.
- The Domain is the x-value of an ordered pair
- The Range is the y-value of an ordered pair
Let's take a look at this table for example
(1,3) (2, 5) (3, 7)
See how each x-value has one y-value? That’s exactly what makes it a function.Every x-value listed on a table or a group of ordered pairs must have one x-value match with one y-value. If you see a number repeating in the x column, then its not a function. Click the next button to see an example of what I mean rookie adventurer.
Next
Look at how the table and the ordered pairs at the bottom have a repeating x-value. This is an example of something that is NOT A FUNCTION, because the x-value is linked to different values. IN A FUNCTION, X-VALUES SHOULD NEVER REPEAT!
(1,3) (2, 5) (3, 7) (1, 2)
Next
Let's Test What We've Learned!
Which of these two tables represents a function?
Ok, so the tables are great and all, but you're probably asking, "How exactly did you come up with the numbers for the table Shaylee?
Here’s the kicker: we didn’t just make them up. We used the function rule.
A function rule is just the instruction or formula that tells you how to get the output (y-value or Range) from the input (x-value or Domain).
A common example would be the Slope a of Line formula: y = mx + b
y is the y-value of a point on the line. m is the slope, which tells you how steep the line is. b is where the line crosses the y-axis.
y = mx + b is just a rule. It tells you, if you pick an x, how to get the y that goes with it. And that… my friends… is exactly what a function does.
Next
You know how a linear equation, such as, y =2x +3, has the letter y at the beginning. A function is the same way but instead of the letter y, we represent with something different Normally, a function is represented by the notation f(x) We can write this same idea in function notation, which looks like this: f(x) = 2x + 3 f(x) just means ‘the output when we put x into the function.’ So instead of saying y, we say f(x). It’s just another name for the output.
Next
For Example: If f(x) = 2x + 3 and x = 1, then f(1) = 2*1 + 3 = 5. That’s exactly the same as saying y = 5 if x = 1. There are lots of ways we can write functions: y = 2x + 3 f(x) = 2x + 3 Even g(t) = 2t + 3 (sometimes we use other letters instead of x)
Next
"Alright, let’s look back at our original table and figure out the function that made these numbers.
Step 1: Look at the x and y pairs. x = 1 → y = 2 x = 2 → y = 4 x = 3 → y = 6 Step 2: Ask yourself, ‘What did we do to x to get y?’ 1 → 2 (multiply by 2) 2 → 4 (multiply by 2) 3 → 6 (multiply by 2) Step 3: Write the rule. Multiply x by 2. In function notation, that’s: f(x) = 2x
Next
"Here’s another way to figure out the function rule, especially if the table looks tricky.
You can pick any two points from the table and find the slope between them. Then use that slope to write the equation.
Step 3: Use point-slope form to write the equation. Formula: y - y1 = m(x - x1) Plug in (1,2) and m = 2 → y - 2 = 2(x - 1) Step 4: Simplify to slope-intercept form. y - 2 = 2x - 2 → So the rule is f(x) = 2x
Step 1: Pick two points from the table.Let’s pick (1, 2) and (2, 4).
Step 2: Find the slope (m). Formula: m = (y2 - y1) / (x2 - x1) m = (4 - 2) / (2 - 1) = 2 / 1 = 2
Next
Let's Test What We've Learned!
"Okay, rookie, one more thing before we start climbing!
Sometimes you’ll be given the graph of a function, and your job could be any of these: Find the function rule – the equation that describes the line. Find f(x) – the output for a given input. Find x – the input that gives a specific output. The graph of a function f is shown. For what value of x is f(x) = 3?’
Click here for the answer
Let's Test What We've Learned!
Try Again?
Final Challenge
Exit
The function table shows points at (0,1), (1,2), (2,4), (3,8). Is this function linear?
A. Yes — linear (growth by equal differences)
B. No — nonlinear (differences are not equal)
C. Not a function
D. Yes — exponential only
Click here for Help
Next
Helpful Hints From Jason
"Hey there! I’m Shaylee’s boyfriend, Jason. If you clicked on this button, that means you need a little bit of help answering this question. Don’t worry—I won’t give you the answer, but here’s a tip to help you figure it out. When you’re trying to figure out which set of points represents a function of x, think about x-values and uniqueness. Each x-value should pair with only one y-value. If any x-value shows up more than once with a different y-value, that set is not a function. Try going through each option slowly, checking the x-values carefully. Look for repeats and see if they point to more than one y. That technique will help you pick the correct set!"
Given the set of ordered pairs {(−1,4),(0,4),(1,5)}, what is the range?
A. {−1, 0 , 1}
B. {4 , 5}
C. {−1, 4, 1, 5, 0}
D. {4}
Click here for Help
A. 7
B. 3
C. 8
D. 5
Click here for Help
Next
Which statement best defines a function?
A. Every input is paired with at least two outputs.
B. Every input has exactly one output.
C. Every output must pair with exactly one input.
D. The graph is always a straight line.
Click here for Help
The Final Challenge!
Click the picture of the Elixir to begin the last challenge. Once you have finished click the next button.
Click the picture
Next
Journey to Function Ridge An Algebraic Odyssey
Yaw Owusu-Akyaw
Created on October 30, 2025
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Transcript
Journey to Function Ridge An Algebraic Odyssey
BackStory
Start Game
Backstory: Enter Dr. Shaylee Owusu
Shaylee Owusu, a brilliant and daring mathematical archaeologist, has spent years studying ancient legends of the Elixir of Infinite Mathematical Knowledge. Hidden atop the perilous cliffs of Function Mountain lies the Apex Domain Shrine, a mysterious place said to grant ultimate understanding of numbers, functions, and equations to those who prove their mastery. Equipped with her climbing gear, sharp mind, and unwavering determination, Shaylee begins her ascent. At each checkpoint along the mountain, she must solve challenging function-based puzzles to continue her climb. Only by reaching the summit and completing the final series of trials at the Apex Domain Shrine can she claim the fabled elixir. Success will reward Shaylee with boundless mathematical insight, while failure risks the Shrine’s magical defenses — powerful energy currents that can sweep away even the most skilled adventurer. Shaylee’s journey is not just a climb of stone and snow, but a test of her intellect, courage, and perseverance. Will she conquer Function Mountain and unlock the secrets of the Apex Domain Shrine, or will the mountain’s challenges prove too great?
Next
Functions Tutorial
A function is basically a rule that connects numbers. You put one number in, the rule does something to it, and you get exactly one number out.
Let's take a look at this table for example
(1,3) (2, 5) (3, 7)
See how each x-value has one y-value? That’s exactly what makes it a function.Every x-value listed on a table or a group of ordered pairs must have one x-value match with one y-value. If you see a number repeating in the x column, then its not a function. Click the next button to see an example of what I mean rookie adventurer.
Next
Look at how the table and the ordered pairs at the bottom have a repeating x-value. This is an example of something that is NOT A FUNCTION, because the x-value is linked to different values. IN A FUNCTION, X-VALUES SHOULD NEVER REPEAT!
(1,3) (2, 5) (3, 7) (1, 2)
Next
Let's Test What We've Learned!
Which of these two tables represents a function?
Ok, so the tables are great and all, but you're probably asking, "How exactly did you come up with the numbers for the table Shaylee?
Here’s the kicker: we didn’t just make them up. We used the function rule.
A function rule is just the instruction or formula that tells you how to get the output (y-value or Range) from the input (x-value or Domain).
A common example would be the Slope a of Line formula: y = mx + b
y is the y-value of a point on the line. m is the slope, which tells you how steep the line is. b is where the line crosses the y-axis.
y = mx + b is just a rule. It tells you, if you pick an x, how to get the y that goes with it. And that… my friends… is exactly what a function does.
Next
You know how a linear equation, such as, y =2x +3, has the letter y at the beginning. A function is the same way but instead of the letter y, we represent with something different Normally, a function is represented by the notation f(x) We can write this same idea in function notation, which looks like this: f(x) = 2x + 3 f(x) just means ‘the output when we put x into the function.’ So instead of saying y, we say f(x). It’s just another name for the output.
Next
For Example: If f(x) = 2x + 3 and x = 1, then f(1) = 2*1 + 3 = 5. That’s exactly the same as saying y = 5 if x = 1. There are lots of ways we can write functions: y = 2x + 3 f(x) = 2x + 3 Even g(t) = 2t + 3 (sometimes we use other letters instead of x)
Next
"Alright, let’s look back at our original table and figure out the function that made these numbers.
Step 1: Look at the x and y pairs. x = 1 → y = 2 x = 2 → y = 4 x = 3 → y = 6 Step 2: Ask yourself, ‘What did we do to x to get y?’ 1 → 2 (multiply by 2) 2 → 4 (multiply by 2) 3 → 6 (multiply by 2) Step 3: Write the rule. Multiply x by 2. In function notation, that’s: f(x) = 2x
Next
"Here’s another way to figure out the function rule, especially if the table looks tricky.
You can pick any two points from the table and find the slope between them. Then use that slope to write the equation.
Step 3: Use point-slope form to write the equation. Formula: y - y1 = m(x - x1) Plug in (1,2) and m = 2 → y - 2 = 2(x - 1) Step 4: Simplify to slope-intercept form. y - 2 = 2x - 2 → So the rule is f(x) = 2x
Step 1: Pick two points from the table.Let’s pick (1, 2) and (2, 4).
Step 2: Find the slope (m). Formula: m = (y2 - y1) / (x2 - x1) m = (4 - 2) / (2 - 1) = 2 / 1 = 2
Next
Let's Test What We've Learned!
"Okay, rookie, one more thing before we start climbing!
Sometimes you’ll be given the graph of a function, and your job could be any of these: Find the function rule – the equation that describes the line. Find f(x) – the output for a given input. Find x – the input that gives a specific output. The graph of a function f is shown. For what value of x is f(x) = 3?’
Click here for the answer
Let's Test What We've Learned!
Functions Tutorial
LET THE ADVENTURE BEGIN!
Next
Level One: Rocky Slope of Variables
"Click and drag Shaylee towards the dot, then click on the finger icon."
Answer this question to continue your journey.
Which of the following sets of points represents a function of x?
A) {(−1, 2), (0, 3), (1, 4)}
B) {(1, 2), (1, 3), (2, 4)}
C) {(-2,0), (0,0), (2,0), (0,1)}
Click here for Help
D) {(0,1), (1,1), (2,1), (3,1)}
Wrong Answer!
Let's Try Again
"Lucky for you I had the helicopter ready, or Shaylee would’ve been snake chow! Now, let’s take this one step at a time. A function is a rule that assigns exactly one output (y-value) to each input (x-value). This means if an x-value appears more than once with different y-values, that set cannot be a function. Let’s look at the options carefully: Option A: {(−1, 2), (0, 3), (1, 4)} — each x-value is unique, so it could be a function. Option B: {(1, 2), (1, 3), (2, 4)} — notice the x-value 1 appears twice with different y-values. That breaks the rule, so it is not a function. Option C: {(-2,0), (0,0), (2,0), (0,1)} — the x-value 0 repeats with two different outputs. This is also not a function. Option D: {(0,1), (1,1), (2,1), (3,1)} — each x-value is unique and maps to one y-value, so this is a function. Often, players focus only on the pattern of the y-values or think a function has to be a straight line — that’s a common mistake. The key is always to check the x-values first. Eliminate any sets where an x-value repeats with a different y-value, then verify the remaining options carefully. That’s how you determine which set represents a function."
Click here to Try Again
Level Two: Cliff of Linear Challenges
"Click and drag Shaylee towards the dot, then click on the finger icon."
Answer the question to continue your journey.
Click here to answer the qeustion
Let's Try Again
*"Luckily, I was climbing close by, right near Shaylee, just in case she got into trouble! Now, let’s carefully think about this question. A function is a rule that assigns exactly one output (y-value) to each input (x-value). That means for every x-value, there can only be one corresponding y-value — no repeats with different outputs. Now, let’s look at the options: A. Every input is paired with at least two outputs. Nope — functions only allow one output per input, so this is wrong. B. Every input has exactly one output. I have hunch this might be what we are looking for. C. Every output must pair with exactly one input. Close, but not required — multiple x-values can share the same y-value. D. The graph is always a straight line. Wrong — functions can be curves, parabolas, or other shapes; they don’t have to be straight lines. A common mistake is to think a function must be a straight line, or to focus on outputs instead of inputs. Always check each input to make sure it only has one output — that’s how you know it’s a function!"
WRONG ANSWER!
Click here to Try Again
Level Three: Boulder Pass of Patterns
"Click and drag Shaylee towards the dot, then click on the finger icon."
Answer the question to continue your journey.
Click here to answer the qeustion
Let's Try Again
We have to hurry before something monsterous eats Shaylee! Alright, let’s break this down carefully. We need to evaluate f(2) for f(x)=2x squared − 1. The key is to follow the order of operations carefully: exponents first, then multiplication, then subtraction. That’s step one — don’t rush it, or we could make a mistake while the carnivores are closing in. Now, let’s look at the options: Option A: 7 — if you properly square the 2 first, multiply by 2, and then subtract 1, this is a strong candidate. Option B: 3 — this might come from forgetting to square first or miscalculating the multiplication. Double-check the order of operations here. Option C: 8 — maybe someone multiplied before squaring, or skipped the subtraction at the end. Think carefully about which step is missing. Option D: 5 — this could happen if subtraction is done incorrectly or if a step in the formula is skipped. Here’s a hint: follow the operations in the right sequence — exponents → multiplication → subtraction. Eliminate the options that don’t follow the proper order, and you’ll narrow it down to the right choice without guessing. Stay focused — every second counts!"
WRONG ANSWER!
Click here to Try Again
Level Four:The Yeti Range
"Click and drag Shaylee towards the dot, then click on the finger icon."
Answer the question to continue your journey.
Click here to answer the qeustion
Let's Try Again
*"Lucky for you I was close by, or those snow yetis would’ve caught you! Let’s look at these points: (0,1), (1,2), (2,4), (3,8). Option A: Yes — linear. Think about whether the differences between outputs are consistent for each step in x. Option B: No — nonlinear. Could the changes in y suggest it’s not constant? Option C: Not a function. Remember, a function only allows one output per input. Option D: Yes — exponential only. Watch for patterns that grow by a factor rather than by equal steps. Check each option carefully, focusing on how the y-values change relative to x-values. That will guide you to the right choice."
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WRONG ANSWER
Level Five: Stormy Peak/ Summit Climb
"Click and drag Shaylee towards the dot, then click on the finger icon."
Answer the question to continue your journey.
Click here to answer the qeustion
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Shaylee almost froze to death up there! Luckily, I was able to set up a base camp near her. Now, let’s take another look at the problem. Remember, the range or output refers to the y-values. Given the set of ordered pairs {(−1, 4), (0, 4), (1, 5)}, what is the range? Option (A) {−1, 0, 1} — This can’t be correct because it lists only the domain, or x-values. Option (B) {4, 5} — This looks promising because we see 4 in both (−1, 4) and (0, 4). Remember, y-values can repeat in a function. Option (C) {−1, 4, 1, 5, 0} — This choice just lists all the numbers we have without identifying which are domain or range. Option (D) {4} — This isn’t correct because there is more than one number in the range for this set of ordered pairs. Check each option carefully, focusing on how the y-values change in relation to the x-values. That will guide you to the correct choice.
Wrong Answer
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Level Five: Stormy Peak/ Summit Climb
"Click and drag Shaylee towards the dot, then click on the finger icon."
"Dr. Shaylee Owusu… You have climbed the frozen heights and braved the shadows of slumbering beasts. Now, your final trial begins." "Before you rests the Elixir of Infinite Mathematical Knowledge — a gift bestowed only to those who prove both wisdom and resolve." "Answer ten questions of logic and number. You must succeed in at least six. Only with a score of sixty percent or higher shall the elixir be yours." "But heed this warning: should you fail… the mountain’s blessing shall become its burden, and a fate of confusion and frustration will shadow your path." "Prepare yourself, student of numbers. The test begins now."
Begin
Click her to begin the final challenge
What was your Final score?
D) 40%
G) 70%
A) 10%
B) 20%
H) 80%
E) 50%
F) 60%
I) 90%
C) 30%
J) 100%
Click here for text to speech
I) 100%
Congratulations!
Shaylee has the Elixir of Infinite Mathematical Knowledge!"
Exit
GAME OVER!
QUICK CLICK HERE!
QUICK CLICK HERE!
Saving D.r Shaylee
Functions Tutorial
A function is basically a rule that connects numbers. You put one number in, the rule does something to it, and you get exactly one number out.
Let's take a look at this table for example
(1,3) (2, 5) (3, 7)
See how each x-value has one y-value? That’s exactly what makes it a function.Every x-value listed on a table or a group of ordered pairs must have one x-value match with one y-value. If you see a number repeating in the x column, then its not a function. Click the next button to see an example of what I mean rookie adventurer.
Next
Look at how the table and the ordered pairs at the bottom have a repeating x-value. This is an example of something that is NOT A FUNCTION, because the x-value is linked to different values. IN A FUNCTION, X-VALUES SHOULD NEVER REPEAT!
(1,3) (2, 5) (3, 7) (1, 2)
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Let's Test What We've Learned!
Which of these two tables represents a function?
Ok, so the tables are great and all, but you're probably asking, "How exactly did you come up with the numbers for the table Shaylee?
Here’s the kicker: we didn’t just make them up. We used the function rule.
A function rule is just the instruction or formula that tells you how to get the output (y-value or Range) from the input (x-value or Domain).
A common example would be the Slope a of Line formula: y = mx + b
y is the y-value of a point on the line. m is the slope, which tells you how steep the line is. b is where the line crosses the y-axis.
y = mx + b is just a rule. It tells you, if you pick an x, how to get the y that goes with it. And that… my friends… is exactly what a function does.
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You know how a linear equation, such as, y =2x +3, has the letter y at the beginning. A function is the same way but instead of the letter y, we represent with something different Normally, a function is represented by the notation f(x) We can write this same idea in function notation, which looks like this: f(x) = 2x + 3 f(x) just means ‘the output when we put x into the function.’ So instead of saying y, we say f(x). It’s just another name for the output.
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For Example: If f(x) = 2x + 3 and x = 1, then f(1) = 2*1 + 3 = 5. That’s exactly the same as saying y = 5 if x = 1. There are lots of ways we can write functions: y = 2x + 3 f(x) = 2x + 3 Even g(t) = 2t + 3 (sometimes we use other letters instead of x)
Next
"Alright, let’s look back at our original table and figure out the function that made these numbers.
Step 1: Look at the x and y pairs. x = 1 → y = 2 x = 2 → y = 4 x = 3 → y = 6 Step 2: Ask yourself, ‘What did we do to x to get y?’ 1 → 2 (multiply by 2) 2 → 4 (multiply by 2) 3 → 6 (multiply by 2) Step 3: Write the rule. Multiply x by 2. In function notation, that’s: f(x) = 2x
Next
"Here’s another way to figure out the function rule, especially if the table looks tricky.
You can pick any two points from the table and find the slope between them. Then use that slope to write the equation.
Step 3: Use point-slope form to write the equation. Formula: y - y1 = m(x - x1) Plug in (1,2) and m = 2 → y - 2 = 2(x - 1) Step 4: Simplify to slope-intercept form. y - 2 = 2x - 2 → So the rule is f(x) = 2x
Step 1: Pick two points from the table.Let’s pick (1, 2) and (2, 4).
Step 2: Find the slope (m). Formula: m = (y2 - y1) / (x2 - x1) m = (4 - 2) / (2 - 1) = 2 / 1 = 2
Next
Let's Test What We've Learned!
"Okay, rookie, one more thing before we start climbing!
Sometimes you’ll be given the graph of a function, and your job could be any of these: Find the function rule – the equation that describes the line. Find f(x) – the output for a given input. Find x – the input that gives a specific output. The graph of a function f is shown. For what value of x is f(x) = 3?’
Click here for the answer
Let's Test What We've Learned!
Try Again?
Final Challenge
Exit
The function table shows points at (0,1), (1,2), (2,4), (3,8). Is this function linear?
A. Yes — linear (growth by equal differences)
B. No — nonlinear (differences are not equal)
C. Not a function
D. Yes — exponential only
Click here for Help
Next
Helpful Hints From Jason
"Hey there! I’m Shaylee’s boyfriend, Jason. If you clicked on this button, that means you need a little bit of help answering this question. Don’t worry—I won’t give you the answer, but here’s a tip to help you figure it out. When you’re trying to figure out which set of points represents a function of x, think about x-values and uniqueness. Each x-value should pair with only one y-value. If any x-value shows up more than once with a different y-value, that set is not a function. Try going through each option slowly, checking the x-values carefully. Look for repeats and see if they point to more than one y. That technique will help you pick the correct set!"
Given the set of ordered pairs {(−1,4),(0,4),(1,5)}, what is the range?
A. {−1, 0 , 1}
B. {4 , 5}
C. {−1, 4, 1, 5, 0}
D. {4}
Click here for Help
A. 7
B. 3
C. 8
D. 5
Click here for Help
Next
Which statement best defines a function?
A. Every input is paired with at least two outputs.
B. Every input has exactly one output.
C. Every output must pair with exactly one input.
D. The graph is always a straight line.
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The Final Challenge!
Click the picture of the Elixir to begin the last challenge. Once you have finished click the next button.
Click the picture
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