IM: 8.5.4: Tables, Equations, and Graphs of Functions (Lesson)

Last updated about 1 year ago

17 questions

4.1: Notice and Wonder: Doubling Back

What do you notice? What do you wonder?

4.2: Equations and Graphs of Functions

The graphs of three functions are shown.

Are you ready for more?

A function inputs fractions a/b between 0 and 1 where a and b have no common factors, and outputs the fraction 1/b. For example, given the input 3/4 the function outputs 1/4, and to the input 1/2 the function outputs 1/2. These two input-output pairs are shown on the graph. 

4.3: Running around a Track

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.

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

Draggable item		Corresponding Item
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.
d=60t, where d is the distance in miles that you would travel in t hours if you drove at 60 miles per hour.

IM: 8.5.4: Tables, Equations, and Graphs of Functions (Lesson)

IM: 8.5.4: Tables, Equations, and Graphs of Functions (Lesson)

What do you notice? What do you wonder?

A function inputs fractions a/b between 0 and 1 where a and b have no common factors, and outputs the fraction 1/b. For example, given the input 3/4 the function outputs 1/4, and to the input 1/2 the function outputs 1/2. These two input-output pairs are shown on the graph.

What do you notice? What do you wonder?

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 a/b between 0 and 1 where a and b have no common factors, and outputs the fraction 1/b. For example, given the input 3/4 the function outputs 1/4, and to the input 1/2 the function outputs 1/2. These two input-output pairs are shown on the graph.

Plot at least 10 more points on the graph of this function.

Are most points on the graph above or below a height of 0.3? Of height 0.01?

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.

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.

Match one of these equations to each of the graphs.

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.

Plot at least 10 more points on the graph of this function.

Are most points on the graph above or below a height of 0.3? Of height 0.01?

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.

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.