Precalc0103to0104-page33

Precalc0103to0104-page33 - be a last resort Here it is a...

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(Section 1.4: Transformations) 1.4.9 PART E: SEQUENCES OF TRANSFORMATIONS Example 9 (Graphing a Transformed Function) Graph y = 2 ± x + 3 . § Solution • We may want to rewrite the equation as y = ± x + 3 + 2 to more clearly indicate the vertical shift . • We will “build up” the right-hand side step-by-step. Along the way, we transform the corresponding function and its graph. • We begin with a basic function with a known graph. (Point-plotting should
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Unformatted text preview: be a last resort.) Here, it is a square root function. Let f 1 x ( ) = x . Basic Graph: y = x Graph: y = x + 3 Begin with: f 1 x ( ) = x Transformation: f 2 x ( ) = f 1 x + 3 ( ) Effect: Shifts graph left by 3 units Graph: y = ± x + 3 Graph: y = ± x + 3 + 2 Transformation: f 3 x ( ) = ± f 2 x ( ) Transformation: f 4 x ( ) = f 3 x ( ) + 2 Effect: Reflects graph about x-axis Effect: Shifts graph up by 2 units...
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