IM 8.5.4 Lesson: Tables, Equations, and Graphs of Functions
What do you notice? What do you wonder?
The graphs of three functions are shown
Match one of these equations to each of the graphs.
, where is the distance in miles that you would travel in hours if you drove at 60 miles per hour.
, where is the number of quarters, and is the number of dimes, in a pile of coins worth $12.50.
, whereis the area in square centimeters of a circle with radius centimeters.
Label each of the axes with the independent and dependent variables and the quantities they represent.
Label each of the axes with the independent and dependent variables and the quantities they represent.
Label each of the axes with the independent and dependent variables and the quantities they represent.
For each function: What is the output when the input is 1?
What does this tell you about the situation? Label the corresponding point on the graph.
Find two more input-output pairs. What do they tell you about the situation? Label the corresponding points on the graph.
A function inputs fractions between 0 and 1 where and have no common factors, and outputs the fraction . For example, given the input the function outputs , and to the input the function outputs . These two input-output pairs are shown on the graph. Plot at least 10 more points on the graph of this function below. Are most points on the graph above or below a height of 0.3?
Plot at least 10 more points on the graph of this function.
Are most points on the graph above or below a height 0.01?
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?
How far had he gone after 6 seconds?
Estimate when he had run 19.5 meters.
Estimate how far he ran in 4 seconds.
Is Kiran's time a function of the distance he has run? Explain how you know.
Priya is running once around the track. The graph shows her time given how far she is from her starting point.
What was her farthest distance from her starting point?
Estimate how long it took her to run around the track.
Estimate when she was 100 meters from her starting point.
Estimate how far she was from the starting line after 60 seconds.
Is Priya's time a function of her distance from her starting point? Explain how you know.