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Unformatted text preview: MAT 111  College Algebra Section 2.5: Shifting, Reﬂecting and Stretching Graphs Objectives: 1. Know how to graph ”new” functions from old using above transformations. 2. To write formulas of functions given their graphs by realizing the above transformations. Throughout this section consider the function f (x) = and the following variations of f : √ g (x) = x − 2 = x 1/2 − 2 √ h(x) = x + 3 = x 1/ 2 + 3 √ s(x) = x − 2 = (x − 2)1/2 √ t(x) = x + 3 = (x + 3)1/2 √ j (x) = − x = −(x)1/2 √ q (x) = −x = (−x)1/2 x 0 1 4 9 f (x) g (x) = 0 1 2 3 √ x−2 √ x Observation: Do you see a relationship between values of g and those of f ? x 0 1 4 9 f (x) h(x) = 0 1 2 3 √ x+3 Observation: Do you see a relationship between values of h and those of f ? Therefore, in general the graph of f (x) + c is . . . and the graph of f (x) − c is . . . x 0 1 4 9 f (x) 0 1 2 3 x k (x) = 2 3 6 11 √ x−2 Observation: Do you see a relationship between the values in the above tables? x 0 1 4 9 f (x) 0 1 2 3 x t(x) = 3 2 1 6 √ x+3 Observation: Do you see a relationship between the values in the above tables? Therefore, in general the graph of f (x + c) is . . . and the graph of f (x − c) is . . . x 0 1 4 9 √ f (x) j (x) = − x 0 1 2 3 Observation: Do you see a relationship between values of j and those of f ? √ x 0 1 4 9 f (x) 0 1 2 3 x q (x) = 0 1 4 9 −x Observation: Do you see a relationship between values in the above tables? Therefore, in general the graph of −f (x) is . . . and the graph of f (−x) is . . . Now consider the following variations of f : √ s(x) = 2 x √ u(x) = 1/2 x √ v (x) = 2x w(x) = √ √ s(x) = 2 x 1√ x 2 1 x 2 x 0 1/2 2 9/2 v (x) = √ 2x x 0 2 8 18 w(x) = 1 x 2 x 0 1 4 9 f (x) = 0 1 2 3 x u(x) = Therefore, in general the graph of cf (x) is . . . and the graph of f (cx) is . . . Examples: 1. Use transformations to sketch the graph of the following functions: (a) g (x) = 2(x − 5)3 − 5 (b) f (x) = −[x + 4] + 5 2. Write the formula for the function graphed below. ...
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 Fall '10
 CarolineBoulis
 Algebra, Transformations, Formulas

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