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Functions

Evaluating and Interpreting Function Notation

Concept

Function Notation

Function notation is a special way to write functions that explicitly shows that is a function of In other words, that depends on Function notation is symbolically expressed as and read of equals Remember that represents the inputs of the function and represents the outputs. Written in function notation, the function becomes Letters other than can be used to name a function. Additionally, function notation can be adjusted when the variable used to represent the input is not For example, a function describing how the value, of a car changes over time, can be expressed as

Method

Evaluating Functions in Function Notation

Evaluating a function means finding the corresponding - or -value, given the other. When the function is given as a function rule, this is done by substituting the given value and solving for the remaining variable.
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Exercise

Given the function evaluate the following statements.

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Solution
Example

To evaluate means to find the value of when To do this, we can substitute into the rule and simplify.
The statement means that when the function's value is
Example

When evaluating we want to find the value of for which equals We begin by replacing with then solve for using inverse operations.
Thus,
Explanation

What does function notation mean?

Interpreting statements in function notation is sometimes necessary. To accomplish this, it's important to understand what the left- and right-hand sides of mean. Suppose the following statement is given. The left-hand side, tells that the input of the function is The right-hand side, means that for the given input value, the output of the function is Additionally, the statement asks

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Exercise

Julianne and Douglas drive from California to New Mexico. During the first four hours of the trip, the function describes the distance in miles they've driven in the number of hours they've been traveling. Interpret the meaning of the following statements.

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Solution
Example

The function notation, gives the distance traveled in time When we write the time spent traveling is hours. Thus, the statement as a whole gives the distance traveled at hours.

Example

Since gives the distance traveled in time, asks the number of hours it takes to travel a distance of miles.

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