What do you notice? What do you wonder?

A graph in a coordinate plane. Horizontal axis, distance from starting line in meters, vertical axis, time in seconds. The graph begins at the origin and increases steadly as it moves right until it reaches 200 comma 40.  The graph then turns and increases steadily as it moves left until it reaches the point 0 comma 74.

The graphs of three functions are shown.

1. Match one of these equations to each of the graphs.
   1. , where is the distance in miles that someone would travel in hours if they drove at 60 miles per hour.
   2. , where is the number of quarters and is the number of dimes in a pile of coins worth \$12.50.
   3. , where is the area in square centimeters of a circle with radius centimeters.
2. Label each of the axes with the independent and dependent variables and the quantities they represent.
3. For each function, answer the following: What is the output when the input is 1? What does this tell you about the situation? Label the corresponding point on the graph.
4. Find two more input-output pairs. What do they tell you about the situation? Label the corresponding points on the graph.

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

   

   A graph in a coordinate plane, horizontal axis, distance in meters, 0 to 24 by threes, vertical axis, time in seconds, 0 to 10 by ones. Graph begins at the origin and moves steadily upward and to the right, passes through ( 3 comma 1)  and ( 18 comma 6 ).

   	0	3	6	9	12	15	18	21	24	27
   	0	1.0	2.0	3.2	3.8	4.6	6.0	6.9	8.09	9.0

   1. How long did it take Kiran to run 6 meters?
   2. How far had he gone after 6 seconds?
   3. Estimate when he had run 19.5 meters.
   4. Estimate how far he ran in 4 seconds.
   5. Is Kiran's time a function of the distance he has run? Explain how you know.

2. Priya is running once around the track. The graph shows her time given how far she is from her starting point.

   

   A graph in a coordinate plane. Horizontal axis, distance from starting line in meters, vertical axis, time in seconds. The graph begins at the origin and increases steadly as it moves right until it reaches 200 comma 40.  The graph then turns and increases steadily as it moves left until it reaches the point 0 comma 74.

   1. What was her farthest distance from the starting line?
   2. Estimate how long it took her to run around the track.
   3. Estimate when she was 100 meters from the starting line.
   4. Estimate how far she was from the starting line after 60 seconds.
   5. Is Priya's time a function of her distance from her starting point? Explain how you know.