WEEK21-COMPARING-LINEAR-AND-NONLINEAR-FUNCTIONSWEEK21-COMPARING-LINEAR

Comparing Linear and Nonlinear Functions

Objectives

Start

Story

Non-Linear Functions

Linear vs Non-Linear

Real-World Examples

Summary

Story

Key Features of Nonlinear Functions

Interpreting Key Features of Non-Linear Functions

variable Rate of change

Curved Graphs

Domain and Range

Comparing Linear and Nonlinear Functions

Linear vs Non-Linear

Example 2: Non-Linear Function

Example 1: Linear Function

y = 2x + 1

y = x²+1

Recap of Real-World Examples

Click here to draw >

Linear Cost

a) Do it for x=0 to x=3 units in a table. b) Plot points on a cartesian plane. c) Interpret the results.

Calculate the total cost of items bought at a fixed price of $5 per unit:

C(x) = 5x

Solution

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Non-Linear Prices

t: Time in years. P(t): Price in 10 thousands of $ dollars. Let's see how price growths over time:

Housing price in Miami changes over time according to the function:

Click here to draw >

Link the functions with their type

• y=-x+1 -> Linear
• f(x)=x²+2x ->Non-Linear
• g(x)=6x ->NLinear
• h(n)=2ⁿ ->Non-Linear

The solution will appear in 30 seconds

y=-x+1

Linear

f(x)=x²+2x

Linear

g(x)=6x

Non-Linear

h(n)=2ⁿ

Non-Linear

Summary

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

9TH-COMPARING-LINEAR-AND-NONLINEAR-FUNCTIONS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

MA.912.F.1: Understand, compare and analyze properties of functions.. MA.912.F.1.6 Compare key features of linear and nonlinear functions each represented algebraically, graphically, in tables or written descriptions. MA.912.F.1.8 Determine whether a linear, quadratic or exponential function best models a given real- world situation.

MATERIAL

It is highly advised to have:

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