b) To fi nd f (0), substitute 0 for x in the function f (x). f (x) 6x 5 f (0) 6(0) 5 0 5 5 f (0) 5 The ordered pair (0, 5) satisfi es f (x) 6x 5. c) To fi nd g(1), substitute 1 for every x in the function g(x). g(x) x2 8x 3 g(1) (1)2 8(1) 3 1 8 3 12 g(1) 12 The ordered pair (1, 12) satisfi es g(x) x2 8x 3. YOU TRY 6 Let f (x) 4x 1 and h(x) 2x2 3x 7. Find the following function values. a) f (5) b) f (2) c) h(0) d) h(3) We can also fi nd function values for functions represented by a set of ordered pairs, a correspondence, or a graph. EXAMPLE 7 Find f (4) for each function. a) f {(2, 11), (0, 5), (3, 4), (4, 7)} b) Domain f Range c) x y 5 y f(x) 3 5 3 1 4 9 2 8 18 Solution a) Since this function is expressed as a set of ordered pairs, fi nding f(4) means fi nding the y-coordinate of the ordered pair with x-coordinate 4. The ordered pair with x-coordinate 4 is (4, 7), so f (4) 7. b) In this function, the element 4 in the domain corresponds to the element 8 in the range. Therefore, f (4) 8. c) To fi nd f (4) from the graph of this function means to fi nd the y-coordinate of the point on the line that has an x-coordinate of 4. Find 4 on the x-axis. Then, go straight up to the graph and move to the left to read the y-coordinate of the point on the graph where the x-coordinate is 4. That y-coordinate is 3. So, f (4) 3. Remember that f(4) indicates that 4 is in the domain of the function. f(4) is equal to the range value that corresponds to 4. x y 5 y f x 5 www.mhhe.com/messersmith SECTION 4.5 Introduction to Functions 205
messersmith_power_intermediate_algebra_1e_ch4_7_10
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