Next we will learn about refl ecting the graph of f (x) x2 about the x-axis. EXAMPLE 3 Graph f (x) x2 and g(x) x2 on the same axes. Solution f(x) x2 x f(x) 0 0 1 1 2 4 1 1 2 4 x y 5 f x x2 5 5 5 g x x2 g(x) x2 x g(x) 0 0 1 1 2 4 1 1 2 4 The tables of values show us that although the x-values are the same in each table, the corresponding y-values in the table for g(x) are the negatives of the y-values in the fi rst table. With the exception of the vertex, all of the y-coordinates of the points on the graph of g are negative. That is why the graph of g(x) x2 is below the x-axis. Each function has a domain of (q, q). The range of f (x) is 0, q), and the range of g(x) is (q, 0. We say that the graph of g is the refl ection of the graph of f about the x-axis. (The graph of g is the mirror image of the graph of f.) Property Reflection about the x-axis Given the graph of any function f (x), if g(x) f (x) then the graph of g(x) will be the refl ection of the graph of f about the x-axis. That is, obtain the graph of g by keeping the x-coordinate of each point on f the same but take the negative of the y-coordinate. In your own words, explain how to reflect the graph of f(x) about the x-axis. YOU TRY 3 Graph g(x) (x 2)2. EXAMPLE 4 Graph g(x) (x 2)2 1. Solution If we compare g(x) to f (x) x2, what do the constants in g(x) tell us about transforming the graph of f (x)? g(x) (x 2)2 1 c c Shift f (x) Shift f(x) right 2. down 1. 656 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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