Section 3.6 Functions 271 So, when x = 3, y = 7 or f (3) = 7 and an ordered pair solution of the equation is (3, 7). Note that this is exactly what we obtain when we evaluate y = 4x - 5 at x = 3. This process is called evaluating a function. ���������������������� Evaluating a Function f (x) at x = k Step 1: If the function is given in terms of an equation, replace the variable with the number k that is given in parentheses and simplify. Step 2: If the function is given in terms of a set, a mapping, or a table, find the y-value that corresponds to the x-value of k. Step 3: If the function is given in terms of a graph, find the ordered pair on the graph whose x-value is k. The corresponding y-value is the result of f (k). �� ������������������������ ������������������ Evaluate each function at the given value. 4a. Find f (0) if f (x) = 3x - 12. 4b. Find g(-3) if g(x) = x2 + 1. 4c. Find c(4) if the function c(x) 4d. Find f (2) if f (x) is given by the is given by Y1. following graph. 2 2 4 –2 –4 –2 –4 –6 x y Solutions 4a. f (0) = 3(0) - 12 = 0 - 12 = -12 4b. g(-3) = (-3)2 + 1 = 9 + 1 = 10 4c. The point (4, -8) is one of the ordered pairs in the table. So, c(4) = -8 4d. The point (2, -4) lies on the graph of the function. So, f (2) = -4. 2 2 4 (2, –4) –2 –4 –2 –4 –6 x y Student Check 4 Evaluate each function at the given value. a. Find f (0) if f (x) = 9x + 4. b. Find g(-5) if g(x) = -2x2 - 4x + 1. c. Find c(2) if the function c(x) is given by Y1. d. Find f (-2) if f (x) is given by the following graph. 2 2 4 –2 –4 –2 –4 –6 x y
hendricks_beginning_algebra_1e_ch1_3
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