Curriculum  /  Math  /  8th Grade  /  Unit 4: Functions  /  Lesson 7

Functions

Lesson 7

Math

Unit 4

8th Grade

Lesson 7 of 12

Objective

Define and graph linear and nonlinear functions.

Common Core Standards

Core Standards

  • 8.F.A.3 — Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Foundational Standards

  • 7.EE.B.4
  • 7.RP.A.2

Criteria for Success

  1. Graph a linear function using a table of values and coordinate points. 
  2. Graph a nonlinear function using a table of values and coordinate points.
  3. Understand that a linear function consists of ordered pairs that, when graphed, lie on a straight line; points on a nonlinear function do not lie on a straight line. 

Tips for Teachers

Lessons 7 and 8 introduce students to linear vs. nonlinear functions. In Lesson 7, students see what examples of linear and nonlinear functions look like as graphs, and in Lesson 8, students will look at examples of functions in all representations and determine if they are linear or nonlinear.

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Anchor Problems

25-30 minutes

Problem 1

It costs $${$4}$$ to enter a carnival and an additional $${$2}$$ for each activity you do once inside the carnival. The equation below represents the total cost spent at the carnival, $$y$$, as a function of the number of activities done, $$x$$.

$$y=2x+4$$

a.   Create a table of values that represents some inputs and their corresponding outputs and use the table of values to sketch a graph of the function.

b.   Does this function appear to be a linear function?

c.   What is the rate of change?

d.   What is the initial value?

Guiding Questions

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Student Response

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Problem 2

The equation below represents the area of a square, $$a$$, as a function of its side length, $$s$$.

$$a=s^2$$

a.   Create a table of values that represents some inputs and their corresponding outputs and use the table of values to sketch a graph of the function.

b.   Does this function appear to be a linear function? Explain.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

A chocolate factory makes 240 chocolates in 6 minutes. The total number of chocolates produced is a function of the number of minutes that the factory is running.

a.   Write an equation that describes the total number of chocolates produced ($$y$$), as a function of the number of minutes ($$x$$) that the factory runs.

b.   Use the equation you wrote in part a to find the number of chocolates produced when the factory runs for 3 minutes, 16 minutes, and 20 minutes.

c.   Plot the points from part b on the graph below.

d.   Is the function linear or nonlinear? Explain how you know.

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Determine if functions are linear or nonlinear when represented as tables, graphs, and equations.

Lesson 8
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Defining Functions

Topic B: Representing and Interpreting Functions

Topic C: Comparing Functions

Topic D: Describing and Drawing Graphs of Functions

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