Unit 1A

Precalculus

Lesson 1: Domain, Range, and Interval Notation

Domain and Range

Thermometers are excellent tools for measuring temperature. Specific types of thermometers are used in specific situations. For example, the thermometer you would use to measure the temperature outside is a different type of thermometer from the one you would use for cooking.

The temperature range of a thermometer is the span from the lowest and to the highest values on the scale.

The thermometer pictured would have a temperature range from «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mo»-«/mo»«mn»40«/mn»«mo»§#160;«/mo»«mo»§#176;«/mo»«mi mathvariant=¨normal¨»C«/mi»«/mrow»«/mstyle»«/math» to «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»50«/mn»«mo»§#160;«/mo»«mo»§#176;«/mo»«mi mathvariant=¨normal¨»C«/mi»«/mstyle»«/math».

The meat thermometer would have a temperature range from «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»20«/mn»«mo»§#160;«/mo»«mo»§#176;«/mo»«mi mathvariant=¨normal¨»C«/mi»«/mstyle»«/math» to «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»100«/mn»«mo»§#160;«/mo»«mo»§#176;«/mo»«mi mathvariant=¨normal¨»C«/mi»«/mstyle»«/math».

The specific type of thermometer used in a situation is selected based on its particular temperature range.

What is domain? What is range? Why are they important?

The domain of a relation is the set of all possible «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math»-values, or input values.

The range of a relation is the set of all possible «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«/mstyle»«/math»-values, or output values.

The output value of a relation, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»y«/mi»«/mstyle»«/math», is calculated when an input value, «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi»x«/mi»«/mstyle»«/math», is substituted into the equation of the relation.

For example, if you were to substitute the input value of «math style=¨font-family:Verdana¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mn»5«/mn»«/mstyle»«/math» in the equation of the linear function


the output value would be as follows: