# UB MTH 309 - 2.5_Transformations_of_Functions (36 pages)

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## 2.5_Transformations_of_Functions

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- Pages:
- 36
- School:
- University at Buffalo, The State University of New York
- Course:
- Mth 309 - Intro Linear Algebra

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Section 2 5 Transformation of Functions Graphs of Common Functions Reciprocal Function y f x 1 x x Domain 0 0 Range 0 0 Decreasing on 0 and 0 Odd function Vertical Shifts Vertical Shifts Let f be a function and c be a positive real number The graph of y f x c is the graph of y f x shifted c units vertically upward The graph of y f x c is the graph of y f x shifted c units vertically downward Vertical Shifts Example Use the graph of f x x to obtain g x x 2 y x Horizontal Shifts Horizontal Shifts Let f be a function and c a positive real number The graph of y f x c is the graph of y f x shifted to the left c units The graph of y f x c is the graph of y f x shifted to the right c units Horizontal Shifts Example Use the graph of f x x2 to obtain g x x 1 2 y x Combining Horizontal and Vertical Shifts Example Use the graph of f x x2 to obtain g x x 1 2 2 y x Reflections of Graphs Refection about the x Axis The graph of y f x is the graph of y f x reflected about the x axis Reflections about the x axis Reflection about the y Axis The graph of y f x is the graph of y f x reflected about y axis Example Use the graph of f x x3 to obtain the graph of g x x 3 y x Example Use the graph of f x x to graph g x x y x Vertical Stretching and Shrinking Vertically Shrinking Vertically Stretching Graph of f x x3 y Graph of g x 3x3 y x x This is vertical stretching each y coordinate is multiplied by 3 to stretch the graph Example Use the graph of f x x to graph g x 2 x y x Horizontal Stretching and Shrinking Horizontal Shrinking Horizontal Stretching Use the graph of f x x to obtain the Example 1 graph of g x x 3 y x f x x x Use the graph of f x x to graph g x x The graph of g x will appear in which quadrant a Quadrant I b Quadrant II c Quadrant III d Quadrant IV g x x Write the equation of the given graph g x The original function was f x x2 2 a g x x 4 3 2 g x x 4 3 b 2 g x x 4 3 c 2 g x x 4 3 d x g x Write the equation of the given graph g x The original function was f x x a g x x 4 b

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