Section 2.7 Graphs of Functions 209 4x 8 f 1x2 f mx b, 1x2 d. is linear. Writing it in the form we get 1 2 where and e. fits none of these categories. Skill Practice Identify each function as constant, linear, quadratic, or none of these. 3. m1x2 2x2 3x 7 4. n1x2 6 5. 6. 4. Finding the x- and y-Intercepts of a Graph Defined by y f(x) In Section 2.1, we learned that to find the x-intercept, we substitute y 0 and solve the equation for x. Using function notation, this is equivalent to finding the real solutions of the equation f (x) 0. To find the y-intercept, substitute and solve the equation for y. In function notation, this is equivalent to finding f (0). Finding Intercepts Using Function Notation Given a function defined by y f (x), Step 1 The x-intercepts are the real solutions to the equation f (x) 0. Step 2 The y-intercept is given by f (0). Finding x- and y-Intercepts Example 4 Given the function defined by f (x) a. Find the x-intercept(s). b. Find the y-intercept. c. Graph the function. Solution: a. To find the x-intercept(s), find the real solutions to the equation f (x) 0. f 1x2 2x 4 2x 4: 0 2x 4 Substitute f 1x2 0. 4 2x 2 x The x-intercept is 12, 02. x 0 R1x2 4 3x 1 2 W1x2 4 3 x 1 2 f 1x2 6 x 2 m b 1. 1 2 x 1, f 1x2 4x 8 8 8 8 Answers 3. Quadratic 4. Constant 5. Linear 6. None of these
miller_intermediate_algebra_4e_ch1_3
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