5.4- Tables, Equations, and Graphs of Functions

5.4- Tables, Equations, and Graphs of Functions

What do you notice? What do you wonder?

Consider what the graph might represent.

Multiple Choice

Which equation would match the graph.

• $d=60t$ where $d$ is the distance in miles that you would travel in $t$ hours if you drove at 60 miles per hour.

• $q=50-0.4d$ , where $q$ is the number of quarters, and $d$ is the number of dimes, in a pile of coins worth $12.50.

• $A=\pi r^2$ , where $A$ is the area in square centimeters of a circle with radius $r$ centimeters.

Multiple Choice

Which equation would match the graph.

• $d=60t$ where $d$ is the distance in miles that you would travel in $t$ hours if you drove at 60 miles per hour.

• $q=50-0.4d$ , where $q$ is the number of quarters, and $d$ is the number of dimes, in a pile of coins worth $12.50.

• $A=\pi r^2$ , where $A$ is the area in square centimeters of a circle with radius $r$ centimeters.

Multiple Choice

Which equation would match the graph.

• $d=60t$ where $d$ is the distance in miles that you would travel in $t$ hours if you drove at 60 miles per hour.

• $q=50-0.4d$ , where $q$ is the number of quarters, and $d$ is the number of dimes, in a pile of coins worth $12.50.

• $A=\pi r^2$ , where $A$ is the area in square centimeters of a circle with radius $r$ centimeters.

Fill in the Blanks

Kiran was running around the track. The graph shows the time, t , he took to run various distances, d . The table shows his time in seconds after every three meters.

How long did it take Kiran to run 6 meters?

Fill in the Blanks

Kiran was running around the track. The graph shows the time, t , he took to run various distances, d . The table shows his time in seconds after every three meters.

How far had he gone after 6 seconds?

Fill in the Blanks

Kiran was running around the track. The graph shows the time, t , he took to run various distances, d . The table shows his time in seconds after every three meters.

Estimate when he had run 19.5 meters.

Fill in the Blanks

Kiran was running around the track. The graph shows the time, t , he took to run various distances, d . The table shows his time in seconds after every three meters.

Estimate how far he ran in 4 seconds.

Fill in the Blanks

Kiran was running around the track. The graph shows the time, t , he took to run various distances, d . The table shows his time in seconds after every three meters.

Is Kiran's time a function of the distance he has run? Explain how you know. Is Kiran's time a function of the distance he has run?

Each representation of a function presents information about the input and output of the function in different ways. Tell students to imagine we have a function with independent variable x and dependent variable y.

• How do we find input-output pairs from a graph of the function?

• What is something you won’t see on the graph of the function?

• If the graph of the function contains the point (18,6) , what else do we know about the function?

Fill in the Blanks

Here is the graph of a function showing the amount of money remaining on a subway fare card as a function of the number of rides taken.

What is the output of the function when the input is 10? On the graph, plot this point and label its coordinates.

Fill in the Blanks

Here is the graph of a function showing the amount of money remaining on a subway fare card as a function of the number of rides taken.

What is the input to the function when the output is 5?

Multiple Choice

Here is the graph of a function showing the amount of money remaining on a subway fare card as a function of the number of rides taken.

What does point P tell you about the situation?

• after 27 rides there will be $7.00 remaining on the ride

• point P doesn't tell me anything

• after spending $27.50 there is $7.00 left on the card

• after 7 rides there will be $27.50 remaining on the card