Connecting Representations of Functions

Elena and Lin are training for a race. Elena runs her mile at a constant speed of 7.5 miles per hour. Lin’s total distances are recorded every minute:

Time (minutes)	Distance (miles)
1	0.11
2	0.21
3	0.32
4	0.41
5	0.53
6	0.62
7	0.73
8	0.85
9	1

Who finished their mile first? This is a graph of Lin’s progress. Draw a graph to represent Elena’s mile on the same axes. For these models, is distance a function of time? Is time a function of distance? Explain how you know.

The output is five less than the input

• y=x-5

• x=y-5

• 5-x+y

• y+x=5

The output is the square of the input

• x=y^2

• y=2x

• y=x-2

• y=x^2

What is the value of y=2x+5, when x=3

• x=3

• y=11

• y=3

• y=22

Write an equation that describes the function

• y=x-8

• x=0+4

• y=4x

• y=4+x

Write an equation that describes the function

• y=x-7

• y=x+7

• y=x*4

• y=x-4

Find the value of y=3x+2; x=0.5

• y= -3.5

• y=2.5

• y=3.5

• y= -4

Find the value y=x/2+9; x=-12

• y= 3.4

• y= 12

• y= -3

• y= 3

The output is three less than the input

• x=y-3

• y=x-3

• y=3-x

• y=3x

Is this a function?  Why or why not?

• No, the domain numbers are repeated.

• No, it passes the Vertical Line Test.

• Yes, it passes the Vertical Line Test.

• Yes, the range numbers are not repeated.