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Algebra 1

4.13.4 Real-World Domain and Range

Algebra 14.13.4 Real-World Domain and Range

4.13.4 Real-World Domain and Range

4.13.4 • Real-World Domain and Range

Activity

A discrete function has distinct separate values in the domain and range, rather than an interval of values.

1. Below is a graph from the previous lesson that graphs the number of students attending a camp and the amount, in dollars, the camp earns. There must be 5 students to hold the camp.

a. What are the xx-values of this function that make up the domain?

b. Why can’t we say the domain is all values from 5 to 16?

c. What are the yy-values of this function that make up the range?

A continuous function refers to a function that does not have any breaks in its graph. The domain and range of a continuous function are often represented by an interval that can be written as an inequality.

2. The graph below represents a continuous function. The function, PP, is the cost of parking in a garage for tt hours. It is represented by the function P(t)=5h+10P(t)=5h+10.

a. What does P(0)P(0) represent?

b. In words, what are the values of the domain?

c. How can you write the domain values as an inequality?

d. In words, what are the values of the range?

e. How can you write the range values as an inequality?

Self Check

Which of the following correctly describes the domain and range of the graph below?

  1. Domain: x > 2
    Range: y > 3


  2. Domain: x ≤ 2
    Range: y ≤ 3


  3. Domain: x ≥ 2
    Range: y ≥ 3


  4. Domain: x ≥ 3
    Range: y ≥ 2

Additional Resources

Domain and Range as Inequalities

Looking at the linear function below, use inequalities to represent the domain and range.

Domain:

Since the domain is all xx-values, look left to right for the least to greatest values.

The smallest xx-value on this linear function is 5, and then the line continues to the right forever.

So, the domain is all values that are at least 5.

As an inequality, write this as x≥5x≥5.

Range:

Since the range is all yy-values, look from the bottom to the top for the least to greatest values.

The smallest yy-value is 0, and then the line continues up forever.

So, the range is all values that are at least 0.

An an inequality, the range is y≥0y≥0.

Try it

Domain and Range as Inequalities

Looking at the linear function below, use inequalities to represent the domain and range.

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