Functions

Lesson 8

Objective

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

Common Core Standards

Core Standards

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  • 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

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  • 7.RP.A.2.B

Criteria for Success

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  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

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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.

Guiding Questions

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Problem 2

Determine which equations below represent linear functions. Be prepared to justify your reasoning. 

Equation 1:   $${y = x^2 +1}$$
Equation 2:   $${y=2x+1}$$
Equation 3:   $${y={x \over 2}}$$
Equation 4:   $${y=x^3}$$

Guiding Questions

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Problem Set

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Target Task

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Problem 1

Which of the equations listed below are linear equations? 

Equation 1:   $${C={2\pi}r}$$
Equation 2:   $${A={\pi}r^2}$$
Equation 3:   $${V={4\over3}{\pi}r^3}$$

  1. Equation 1 only
  2. Equation 2 only
  3. Equations 1 and 3
  4. Equations 2 and 3

References

EngageNY New York State Testing Program Grade 8 Common Core Mathematics Test Released Questions May 2016Question 7

From EngageNY.org of the New York State Education Department. New York State Testing Program Grade 8 Common Core Mathematics Test Released Questions May 2016. Internet. Available from https://www.engageny.org/resource/released-2016-3-8-ela-and-mathematics-state-test-questions/file/148616; accessed Oct. 27, 2017, 10:44 a.m..

Problem 2

Complete the table so it represents a linear function. 

$$x$$ $$y$$
2 0
4  
5 18
7  

Mastery Response

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