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


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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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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Problem Set

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Target Task


Problem 1

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

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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.

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Lesson 7

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Lesson 9

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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