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Transformation of Functions Sec. 1.7 Objective You will learn how to identify and graph transformations.

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Important Vocabulary Vertical Shift – the parent graph shifts up or down Horizontal Shift – the parent graph shifts left or right Nonrigid Transformations – the size of the parent graph changes but the shape remains the same

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Shifting Graphs Vertical shift c units upward: Vertical shift c units downward: Horizontal shift c units to the right: Horizontal shift c units to the left:

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Example Write the equation for the function resulting from a vertical shift of 3 units downward and a horizontal shift of 2 units to the right of the graph of f(x).

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Example Use the graph of to sketch the graph of each function. a.)

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Example Use the graph of to sketch the graph of each function. b.)

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A family of functions is… A set of functions (or graphs) that have the same shape but are at a different location in the plane.

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Reflecting Graphs A reflection in the x-axis is a type of transformation of the graph represented by. A reflection in the y-axis is a type of transformation of the graph represented by.

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Example Let. Describe the graph of in terms of f.

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Example The function g(x) shown in the figure is a transformation of the graph of. Find an equation for the function g(x).

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Example Compare the graphs of each function with the graph of a.) b.) The graph of g(x) is a reflection of f(x) across the x-axis. The graph of h(x) is a reflection of f(x) across the x-axis, and it is shifted left two units.

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Rigid Transformations A rigid transformation is a transformation that does not alter the size or shape of a function. Rigid transformations change only the position of the graph in the xy-plane. Types of rigid transformations: Horizontal shifts Vertical shifts Reflections

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Nonrigid Transformations Types of nonrigid transformations: Vertical stretch Vertical shrink Horizontal stretch Horizontal shrink

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Nonrigid Transformations A vertical stretch is represented by where c >1. A vertical shrink is represented by where 0< c <1. A horizontal shrink is represented by where c >1. A horizontal stretch is represented by where 0< c <1.

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Example Compare the graph of each function with the graph of a.) b.) The graph of g(x) is a vertical stretch of f(x). The graph of h(x) is a vertical shrink of f(x).

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Example Compare the graph of each function with the graph of a.) The graph of g(x) is a horizontal shrink of f(x). Compare

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Example Compare the graph of each function with the graph of b.) The graph of h(x) is a horizontal stretch of f(x). Compare

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Practice Problems Sec. 1.7, page 72 – 75 # 21 – 45 every other odd

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