YOU TRY 2 Use the vertical line test to determine whether each relation is also a function. Then, identify the domain and range. a) x y 5 5 5 5 b) x y 5 (4, 3) 5 5 5 2 Given an Equation, Determine Whether y Is a Function of x and Find the Domain We can also represent relations and functions with equations. The example given at the beginning of the section illustrates this. The equation y 60x describes the distance traveled (y, in miles) after x hours of driving at 60 mph. If x 2, y 60(2) 120. If x 3, y 60(3) 180, and so on. For every value of x that could be substituted into y 60x there is exactly one corresponding value of y. Therefore, y 60x is a function. Furthermore, we can say that y is a function of x. In the function described by y 60x, the value of y depends on the value of x. That is, x is the independent variable and y is the dependent variable. Property y Is a Function of x If a function describes the relationship between x and y so that x is the independent variable and y is the dependent variable, then we say that y is a function of x. EXAMPLE 3 Determine whether each relation describes y as a function of x. a) y x 2 b) y2 x Solution a) To begin, substitute a couple of values for x and solve for y to get an idea of what is happening in this relation. x 0 x 3 x 4 y x 2 y x 2 y x 2 y 0 2 y 3 2 y 4 2 y 2 y 5 y 2 The ordered pairs (0, 2), (3, 5), and (4, 2) satisfy y x 2. Each of the values substituted for x has one corresponding y-value. In this case, when any value is substituted for x there will be exactly one corresponding value of y. Therefore, y x 2 is a function. www.mhhe.com/messersmith SECTION 4.5 Introduction to Functions 201
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