Linear Functions

Identifying Linear Functions

100

What is a function whose graph forms a straight line called?

linear function

200

What test do we use to determine if a relation is a function?

The Vertical Line Test.

300

Describe two examples of graph that is not a function. (draw a picture if necessary)

Horizontal and U-shape

400

Tell whether the set of ordered pairs satisfies a linear function. Explain (2,4), (5,3) (8,2), (11,1)

Yes, constant change in 3 for x. Constant change of -1 in y

500

Is the following a linear function, explain why or why not.

y=8+ 4x²

No, because it contains an exponent which changes the shape.  It becomes a U shape.

Function Tables

100

A table that organizes the input and output of a function is called what?

Function Table

200

What values does the input and output refer to?

Input= X, Output=Y

300

Complete the table with the following expression:
 y=0.5+3

 Input  | Output
   -2     |    ?
    2     |    ?
    6     |    ?

2, 4, 6

400

Complete the table with the following expression:
 y=-4x - 3

Input  | Output
   -1     |    ?
    3     |    ?
    5     |    ?

1, -15, -23

500

*RANDOM*

What was the final score in last night's Superbowl? Please specify each team with their respective score

Kansas City: 22

Philadelphia: 40

Slope

100

What is the slope of a horizontal line?

Zero

200

What lines have the same slope?

parallel

300

Find the slope of (4,-2) and(-1,2)

What is -4/5

400

Find the slope of (20,3000) and (60,2000)

What is -25

500

Find the slope of the equation: 6x + 5y=30

What is 6/5

Constructing Linear Functions

100

What does the letter b refer to in a slope-intercept for equation?

y-intercept

200

What is the y-intercept of the following equation: y= 4x-3

b= -3

300

Write an equation in slope-intercept form with the following information:

Initial value = 75
Rate of change= 25

y=25x+75

400

Write an equation of the function:
A skiing instructor charges an initial fee plus $30 per hour for lessons.  Sam paid $250 for six hours of instruction. 

y=30x+70

500

What is the y-intercept of the line when: slope=4 and (2,5) is on the line.

b=-3

Compare Functions

100

What two values do we look at when comparing functions?

Initial Value and Rate of Change, or slope and y-intercept

200

If cell phone company A charges $0.25 per gigabyte of data and company B charges $0.23.  Which company will be more expensive to use?

Company A

300

Compare the functions two dog walking services.  Which service would be cheaper to use after 7 days? Explain how you know.

A: y=14x + 25

B: y=13.5x + 30

Company A, because after 6 days of using their service, it would cost $109 which is $2 less than B. 

 Plug in 6 for x and solve for y.

400

Compare the initial values and rates of change. 

Fitness center A charges $32 per month, with a start-up fee of $100.  

Fitness center B is shown in the table.
     x    |     y
    2     |    80
    3     |    120
    4     |    160

 

Fitness center A: initial value = 100, and rate of change = 32

Fitness center B: initial value = 0, and rate of change= 40

Fitness center A costs more upfront and is cheaper per month.  Fitness center B costs $0 upfront and is $8 more that A every month.

500

Explain why the graph of the function y=7x+3 will never intersect with the graph y=7x+10

Both functions have the same slope but different initial values.  This means that they are parallel lines and will never intersect.