In the problem from the introduction, a fan in the stands timed a baseball player as he ran from one base to the next. As a result, he produced the following set of ordered pairs.

{(90, 3.8), (180, 8.0), (270, 12.5), (360, 17.4)}

As you recall from Algebra 1, the domain is the set of input values of a function or relation, and the range is the set of output values.

The input and output values from the problem above have been placed randomly below. Drag each one to the domain or range as is appropriate. Remember, values in the domain and range set should be listed in order from least to greatest.

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The domain is the set of independent values and, if graphed, can be found along the horizontal axis. The range is the set of dependent values and, if graphed, can be found along the vertical axis.

### Conclusion Questions

• What do the values in the domain represent in the baseball problem?

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The domain represents the total distance in feet that the player ran from home plate to first, second, third, and back to home plate. It is 90 feet from home to first base, 180 feet from home to second base, 270 feet from home to third base, and 360 feet from home plate back to home plate.

• What do the values in the range represent in the baseball problem?

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The range represents the time in seconds it took the player to run to each base from home plate. It took him 3.8 seconds to reach first base. The elapsed time to second base was 8.0 seconds. His time to third base was 12.5 seconds. The total time that it took him to return to home plate was 17.4 seconds.

### Pause and Reflect

The domain consists of values that represent the independent variable, and the range consists of values that represent the dependent variable. In the baseball problem above, what are the independent and dependent variables?

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The independent variable is d, the total distance measured in feet that the player ran from home plate to first, second, and third base before returning to home plate. The dependent variable is the total time, t, in seconds that the player took to reach each of the bases.

### Practice

1. State the domain and range of the set of ordered pairs below.

{(3, -5), (5, -6), (2, 8), (3, 10), (-2, -7)}

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Each x-value is a member of the domain, and each y-value is a member of the range.
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D: {-2, 2, 3, 5}; R: {-7, -6, -5 , 8, 10}
2. The average high temperatures for the summer months in Austin, TX, are represented in the ordered pairs below. State the domain and range of the set.

{(Jun, 92.1), (Jul, 95.6), (Aug, 97.0)}

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The domain is the first item in the ordered pair, which is also called the independent variable. The range is the second item in the ordered pair, which is also called the dependent variable.
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D: {Jun, Jul, Aug}; R: {92.1, 95.6, 97.0}
3. What is the domain of this set? {(2 over 3 - 2 3 , 2 over 3 - 2 3 ), (0, 1), (2 over 5 2 5 , 2), (1,7 over 2 7 2 )}

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The domain is the first number in the ordered pair, which is also the x-value.

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D = {2 over 3 2 3 , 0, 2 over 5 2 5 , 1}