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Graphs of Functions

4.13.2 Graphs of Functions

4.13.2 • Graphs of Functions

Activity

For questions 1 – 4, you will be provided with descriptions of four functions and four graphs representing the situation described below.

A child gets on a swing in a playground, swings for 30 seconds, and then gets off the swing.

A young girl with her hair tied up in a bun swings high on a playground swing, facing away from the camera towards the lush green trees and a winding path.

The independent variable in each function is time, measured in seconds.

1. Examine Graph A below.

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Which function description best matches the representation provided in the graph? Be prepared to explain how you made your match.

  1. Function hh: The height of the swing, in feet, as a function of time since the child gets on the swing
  2. Function rr: The amount of time left on the swing as a function of time since the child gets on the swing
  3. Function dd: The distance, in feet, of the swing from the top beam (from which the swing is suspended) as a function of time since the child gets on the swing
  4. Function ss: The total number of times an adult pushes the swing as a function of time since the child gets on the swing

Function rr: The amount of time left on the swing as a function of time since the child gets on the swing

2. Examine Graph B below.

.

Which function description best matches the representation provided in the graph? Be prepared to explain how you made your match.

  1. Function hh: The height of the swing, in feet, as a function of time since the child gets on the swing
  2. Function rr: The amount of time left on the swing as a function of time since the child gets on the swing
  3. Function dd: The distance, in feet, of the swing from the top beam (from which the swing is suspended) as a function of time since the child gets on the swing
  4. Function ss: The total number of times an adult pushes the swing as a function of time since the child gets on the swing

Function ss: The total number of times an adult pushes the swing as a function of time since the child gets on the swing

3. Examine Graph C.

.

Which function description best matches the representation provided in the graph? Be prepared to explain how you made your match.

  1. Function hh: The height of the swing, in feet, as a function of time since the child gets on the swing
  2. Function rr: The amount of time left on the swing as a function of time since the child gets on the swing
  3. Function dd: The distance, in feet, of the swing from the top beam (from which the swing is suspended) as a function of time since the child gets on the swing
  4. Function ss: The total number of times an adult pushes the swing as a function of time since the child gets on the swing

Function dd: The distance, in feet, of the swing from the top beam (from which the swing is suspended) as a function of time since the child gets on the swing

4. Examine Graph D.

.

Which function description best matches the representation provided in the graph? Be prepared to explain how you made your match.

  1. Function hh: The height of the swing, in feet, as a function of time since the child gets on the swing
  2. Function rr: The amount of time left on the swing as a function of time since the child gets on the swing
  3. Function dd: The distance, in feet, of the swing from the top beam (from which the swing is suspended) as a function of time since the child gets on the swing
  4. Function ss: The total number of times an adult pushes the swing as a function of time since the child gets on the swing

Function hh: The height of the swing, in feet, as a function of time since the child gets on the swing

For questions 5 – 8, continue to use the scenario from above and include the following information to determine the domain and range for each function.

  • The child is given 30 seconds on the swing.
  • While the child is on the swing, an adult pushes the swing a total of 5 times.
  • The swing is 1.5 feet (18 inches) above ground.
  • The chains that hold the seat and suspend it from the top beam are 7 feet long.
  • The highest point that the child swings up to is 4 feet above the ground.

[Hint: It may be helpful to revisit the scenario, the matched graph, and the additional list of information to identify specific values for the domain and range.]

5. Describe the domain and range for function hh: The height of the swing, in feet, as a function of time since the child gets on the swing.

  • The domain is time in seconds, so it includes all numbers from 0 to 30.
  • The range represents the height of the swing in feet so it includes all numbers from 1.5 to 4.

6. Describe the domain and range for function rr: The amount of time left on the swing as a function of time since the child gets on the swing.

  • The domain is time in seconds, so it includes all numbers from 0 to 30.
  • The range represents the amount of time left the child has to swing, in seconds, so it includes all numbers from 0 to 30.

7. Describe the domain and range for function dd: The distance, in feet, of the swing from the top beam (from which the swing is suspended) as a function of time since the child gets on the swing.

  • The domain is time in seconds, so it includes all numbers from 0 to 30.
  • The range represents the distance of the swing from the top beam in feet so it includes only one value, 7.

8. Describe the domain and range for function ss: The total number of times an adult pushes the swing as a function of time since the child gets on the swing.

  • The domain is time in seconds, so it includes all numbers from 0 to 30.
  • The range represents the total number of times an adult pushes the swing so it includes only the whole numbers from 0 to 5.

Self Check

Which of the following is true about the range of the graph below?

A graph. 

  1. The range of this function only includes 10 and 75.
  2. The range of this function includes all values that are at least 10 and at most 75.
  3. The range of this function includes all values that are at least 0 and no more than 90.
  4. The range of this function includes all values that are at least 0 and no more than 70.

Additional Resources

Describing Domain and Range Graphs

In a previous lesson, you explored the height, hh, of a bungee jumper at tt seconds.

A graph showing height (h, in meters) versus time (t, in seconds). The curve starts high, then oscillates with decreasing and then steady amplitude as time increases.

Assuming the jump ended at 35 seconds, what is the domain?

For domain, consider the xx-values, so look from left to right.

The leftmost xx-value is 0, and the rightmost xx-value is 35.

The domain includes all the values from at least 0 up to and including 35 meters.

What are the values in the range?

For the range, consider the yy-values, so look from bottom to top.

The lowest yy-value is 10, and the highest yy-value is about 75.

So, the range includes all of the values from at least 10 up to about 75.

Try it

Try It: Describing Domain and Range Graphs

Describe the values of the domain and range using the graph below.

A graph shows the height of an object over time, starting at (0, 20), peaking at (1, 25), and hitting the ground at (3.2, 0). The x-axis is time in seconds; the y-axis is height in meters.

Your answers may vary, but here are some examples:

Here is how to find the domain and range values of this function:

For the domain, consider the xx-values on the graph.

The domain includes all of the values from at least 0 through and including 3.2.

For the range, consider the yy-values on the graph.

The range includes all of the values from at least 0 through and including 25.