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Shifting, Reflecting, and Stretching Graphs

Some Basic Graphs. ConstantIdentityAbsolute Value. Square RootQuadraticCubic. Vertical Shifts. Suppose c is a positive number and f(x) is a given functionh(x) = f(x) c is a shift upward by c units.h(x) = f(x) ? c is a shift downward by c units. . Horizontal Shifts. Suppose c is a positiv

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Shifting, Reflecting, and Stretching Graphs

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    1. Shifting, Reflecting, and Stretching Graphs

    2. Some Basic Graphs Constant Identity Absolute Value Square Root Quadratic Cubic

    3. Vertical Shifts Suppose c is a positive number and f(x) is a given function h(x) = f(x) + c is a shift upward by c units. h(x) = f(x) – c is a shift downward by c units.

    4. Horizontal Shifts Suppose c is a positive number and f(x) is a given function. h(x) = f(x-c) is a shift right by c units. h(x) = f(x+c) is a shift left by c units.

    5. Reflections If y = f(x) is a given function, h(x) = -f(x) is a reflection through the x-axis. h(x) = f(-x) is a reflection through the y-axis.

    6. Nonrigid Transformations Suppose y = f(x) is a given function, and a is a positive real number. h(x) = af(x) stretches the graph vertically if a > 1 If 0 < a < 1, the graph is compressed.

    7. Nonrigid Transformations If a < 0, in addition to the effects on the previous slide, the graph is reflected through the x-axis.

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