3.2-3.3 Linear Functions & Function Notation

Linear Functions & Function

Notation

3.2-3.3

Learning Target

Student will be able to…
● identify linear functions using graphs, tables, and equations.
● graph and write linear functions.

Multiple Choice

Find a set of domains and range of each ordered pair and determine whether it is a function or not.

• Domain: {-2,-1,0,1,1}

  Range: {1,2,3,4,5}

  No, it's not a function

• Domain: {1,2,3,4,5}

  Range: {-2,-1,0,1,1}

  Yes, it's a function

Multiple Choice

Find a set of domains and range of each ordered pair and determine whether it is a function or not.

$$\left\{\left(1,2\right),\left(5,8\right),\left(9,-4\right)\right\}$$

• Domain: {2,8,-4}

  Range: {1,5,9}

  No, it's not a function

• Domain: {1,5,9}

  Range: {2,8,-4}

  Yes, it's a function

• ​it's also written in a slope in the slope intercept form: y=mx+b

Example 1

Identifying linear functions using graphs.
Does the graph represent a linear or nonlinear function? Explain.

Example 2

Identifying linear functions using tables.
Does the table represent a linear or nonlinear function? Explain.

Example 3

Given function g(x)=5–2x, find the range.

a)

g(-1)

b)

g(2)

c)

g(-34)

Example 4

Find the domain (x) for the range given.

a)

f(x)=10

b) f(x)=-12

f(x)=3x-2

f(x)=-2x+6

Example 5

Multiple Choice

Does the graph represent linear or nonlinear function? Why or why not?

• It is a linear function,

  because the graph forms by two straight lines.

• It is a nonlinear function, because the graph is a V-shape which is an absolute value function.

• It is a linear function, because the domain value is not repeating.

• It is a linear function, because it passes the vertical line test