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Algebra 1

4.13.3 Finding Domain and Range Using a Graph

Algebra 14.13.3 Finding Domain and Range Using a Graph

4.13.3 Finding Domain and Range Using a Graph

4.13.3 • Finding Domain and Range Using a Graph

Activity

A tennis ball was dropped from a certain height. It bounced several times, rolled along for a short period, and then stopped. Function H H gives its height over time.

Here is a partial graph of H H . Height is measured in feet. Time is measured in seconds.

Use the graph to help you answer the questions.

Be prepared to explain what each value or set of values means in this situation.

1. Find H ( 0 ) H ( 0 ) . What point is this on the graph? What does it represent?

2. Solve H ( x ) = 0 H ( x ) = 0 .

3. Describe the domain of the function.

4. Describe the range of the function.

Are you ready for more?

Extending Your Thinking

In function H H , the input was time in seconds, and the output was height in feet.

Think about some other quantities that could be inputs or outputs in this situation.

1. Describe a function whose domain includes only integers. Be sure to specify the units.

2. Sketch a graph of this function.

3. Describe a function whose range includes only integers. Be sure to specify the units.

4. Sketch a graph of this function.

Video: Interpreting Function Notation

Watch the following video to learn more about function notation.

4.13.3

Self Check

The graph below shows the number of customers, C , in a restaurant x hours after 8 a.m.

What does C ( 14 ) equal, and what does it mean?

  1. C ( 14 ) = 0 means there have not been any customers over 14 hours.
  2. C ( 14 ) = 0 and means there are 14 customers at 8 a.m.
  3. C ( 14 ) = 0 and is when the restaurant closes and has no more customers around 10 p.m.
  4. C ( 14 ) = 0.5 and means there are 14 customers around 8:30.

Additional Resources

Domain and Range from Graphs

The graph below shows the distance Carl drives from home, D ( t ) D ( t ) , when t t is time in seconds.

1. What is the domain of the graph?

2. What is the range of the graph?

3. What are the values of x x where D ( x ) = 0 D ( x ) = 0 , and what do they mean?

Try it

Domain and Range from Graphs

What are the values for the domain and range of the graph below?

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