WEEK 18-INCREASING-AND-DECREASING-FUNCTIONS

Increasing and Decreasing Functions

Objectives

Start

Intuition of ↗ ↘ Functions

Definitions

Classification Examples

Practice

Summary

Intuition of Increasing and Decreasing Functions

Increasing and decreasing functions can be seen as ascending and descending from a mountain.

🗨️

Decreasing

Increasing

Definitions of Increasing and Decreasing Functions

Definition: A function is called increasing if, as x increases, y also increases.

Example: is an increasing function, as long as its slope is +2.

y=2x+1

Definition: A function is called decreasing if, as x increases, y decreases.

Example: is a decreasing function, as long as its slope is -1.

y=-x+5

Classification Examples

Let's see some examples:

Example 2: A function goes like for . Determine if it's an increasing or decreasing function.

Example 1: A roller coaster cart is moving as shown in the animation. Overall, is it on an increasing or a decreasing function?

f(x)=x²/2

x≥0

Increasing function

It is neither an increasing nor a decreasing function

Practice

Try it by yourself:

Click here to draw >

Variable market prices

Consider the example where the number of computers sold q is a function of price p as follows:

b) Graph units versus price. Is the units an increasing or decreasing function?

q(p)=-3p+100

a) Fill the table:

Increasing

Decreasing

Click here to draw >

Variable market prices

Determine where the function is increasing and decreasing.

b) Graph the function and determine where it increases or decreases:

a) Create a table of values for the function.

Solution

Summary: Classification of Functions

NONE OF THEM

INCREASING

DECREASING

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

8TH-INCREASING-AND-DECREASING-FUNCTIONS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

MATERIAL

It is highly advised to have:

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A compass.
• A Protactor.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).

"MA.8.F.1 Define, evaluate and compare functions." MA.8.F.1.3 "Analyze a real-world written description or graphical representation of a functional relationship between two quantities and identify where the function is increasing, decreasing or constant." "MA.8.AR.3 Extend understanding of proportional relationships to two-variable linear equations." MA.8.AR.3.5 Given a real-world context, determine and interpret the slope and y-intercept of a two-variable linear equation from a written description, a table, a graph or an equation in slope-intercept form. MA.K12.MTR.7.1 Apply mathematics to real-world contexts. ELA.K12.EE.2.1 Read and comprehend grade-level complex texts proficiently.