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

Functions

Lesson 8

Math

Unit 4

8th Grade

Lesson 8 of 12

Objective

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

Common Core Standards

Core Standards

  • 8.F.A.1 — Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8.
  • 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.RP.A.2.B

Criteria for Success

  1. Determine if a function represented as a table or coordinate points is linear.
  2. Determine if a function represented as an equation is linear.
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Anchor Problems

25-30 minutes

Problem 1

The tables below show some input and output values for two different functions. 
Determine if each table represents a linear or nonlinear function.

a.   Table A

$$x$$ $$y$$
2 6
3 8
5 12
8 18

b.   Table B

$$x$$ $$y$$
1 3
2 5
3 8
5 17

Guiding Questions

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Student Response

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Problem 2

Determine if each equation below represents a linear or nonlinear function. Be prepared to justify your reasoning. 

a.    Equation 1:   $${y = x^2 +1}$$

b.    Equation 2:   $${y=2x+1}$$

c.    Equation 3:   $${y={x \over 2}}$$

d.    Equation 4:   $${y=x^3}$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

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Target Task

5-10 minutes

Problem 1

Which of the following equations are nonlinear? Choose all that apply.

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Student Response

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Problem 2

Complete the table so it represents a linear function.

$$x$$ $$y$$
2 0
4  
5 18
7  

 

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

Compare functions represented in different ways (Part 1).

Lesson 9
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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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