221 2.3 Functions Find the center-radius form of the circle described or graphed. (See Exercises 57–62.) 63. a circle having a diameter with endpoints 1-1, 22 and 111, 72 64. a circle having a diameter with endpoints 15, 42 and 1-3, -22 65. 0 (1, 4) (5, 1) x y 66. 0 (–3, 10) (5, –5) x y 2.3 Functions ■ Relations and Functions ■ Domain and Range ■ Determining Whether Relations Are Functions ■ Function Notation ■ Increasing, Decreasing, and Constant Functions Relations and Functions As we saw previously, one quantity can sometimes be described in terms of another. • The letter grade a student receives in a mathematics course depends on a numerical score. • The amount paid (in dollars) for gas at a gas station depends on the number of gallons pumped. • The dollars spent by the average American household depends on the expense category. We use ordered pairs to represent these corresponding quantities. For example, 13, $10.502 indicates that we pay $10.50 for 3 gallons of gas. Since the amount we pay depends on the number of gallons pumped, the amount (in dollars) is called the dependent variable, and the number of gallons pumped is called the independent variable. Generalizing, if the value of the second component y depends on the value of the first component x, then y is the dependent variable and x is the independent variable. Independent variable Dependent variable 1x, y2 A set of ordered pairs such as 513, 10.502, 18, 28.002, 110, 35.0026 is a relation. A function is a special kind of relation. Relation and Function A relation is a set of ordered pairs. A function is a relation in which, for each distinct value of the first component of the ordered pairs, there is exactly one value of the second component. NOTE The relation from the beginning of this section representing the number of gallons of gasoline and the corresponding cost is a function because each x-value is paired with exactly one y-value.
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