178 Chapter 3 Graphs, Relations, and Functions SECTION 3.3 Functions To introduce this concept, consider cell phone numbers and the person assigned to the number. If we think of the phone number as the input and the person assigned to the number as the output, we have a relation with ordered pairs of the form (number, person). This relation satisfies the definition of a function since each input value corresponds to only one output value. That is, each x-value corresponds to only one y-value. There would be complete chaos if a cell phone number was assigned to more than one person! Since a function is a special relation, functions can also be expressed as a set of ordered pairs, a mapping, an equation, a table, or a graph. Consider the set of ordered pairs {(1, 3), (2, 4), (3, 4), (4, 6)}. We can use a mapping to visualize that each x-value corresponds to exactly one y-value. Therefore, the mapping is a function. Now consider the following table. The input 3 4 6 1 2 3 4 value of 12 corresponds to two different output values—Aisha and Hussein. Therefore, this relation is not a function. Credit Hours Student 12 Aisha 6 Juan 12 Hussein 15 Rose Finally, we will consider a relation defined by the equation, y = 5x + 2 . Note that each input value is multiplied by 5 and then added to 2, so there is only one possible output value. So, this equation is a function. Note: If there is only one corresponding y-value for each x-value, then the relation is a function. If at least one x-value corresponds to more than one y-value, then the relation is not a function. ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Determine if a relation is a function. 2. Use the vertical line test. 3. Use function notation. 4. Apply functions to real life. 5. Troubleshoot common errors. According to the U.S. Department of Labor, the fastest-growing occupation for the years 2006–2016 is a network system and data communications analyst. The function f (x) = 1343x + 45,657 approximates the median salary for x years of experience. (Source: http://www.bls.gov and http://www.payscale.com) In this section, we will learn the definition of a function and how to use functions to obtain certain information. Functions In Section 3.2, we defined a relation as a set of ordered pairs, a correspondence between a set of input values and output values. A function is a special type of relation. Definition: A function is a relation in which each member of the domain (or each input) corresponds to exactly one member of the range (or an output). In other words, each input, or x-value, can have only one output, or y-value. Objective 1 ▶ Determine if a relation is a function.
hendricks_intermediate_algebra_1e_ch1_3
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