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Section 1.4 Shifting, Reflecting, and Stretching Graphs

Six important functions: Graph?? ?? =???? ?? =???? ?? = ?? ?? ?? = ?? 2 ?? ?? = ?? 3 ?? ?? = ?? . Use a graphing utility to graph Y1 = f(x) = x2. Then, on the same viewing screen, graph Y2 = (x ? 4)2Y3 = (x 4)2Y4 = x2 4Y5 = x2 ? 4.. Vertical and Horizontal Shifts. Let c be a positiv

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Section 1.4 Shifting, Reflecting, and Stretching Graphs

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    1. Section 1.4 Shifting, Reflecting, and Stretching Graphs Students will know how to identify and graph shifts, reflections, and non-rigid transformations of functions.

    2. Six important functions: Graph ?? ?? =?? ?? ?? =?? ?? ?? = ?? ?? ?? = ?? 2 ?? ?? = ?? 3 ?? ?? = ??

    3. Use a graphing utility to graph Y1 = f(x) = x2. Then, on the same viewing screen, graph Y2 = (x 4)2 Y3 = (x + 4)2 Y4 = x2 + 4 Y5 = x2 4.

    4. Vertical and Horizontal Shifts Let c be a positive real number. The following changes in the function y = f(x) will produce the stated shifts in the graph of y = f(x). 1. h(x) =f(x c) Horizontal shift c units to the right 2. h(x) =f(x + c) Horizontal shift c units to the left 3. h(x) =f(x) c Vertical shift c units downward 4. h(x) =f(x) + c Vertical shift c units upward

    5. Example 1. Given f(x) = ?? 3 , describe the shifts in the graph of f generated by the following functions. g(x) = (??+1) 3 +2 h ?? = (??-4) 3

    6. Reflecting Graphs On your calculator graph ?? 1 = f(x) = (??-2) 3 . Graph ?? 1 = f(x) = -(??-2) 3 . Graph ?? 1 = f(x) = (-??+2) 3 .

    7. The following changes in the function y = f(x) will produce the stated reflections in the graph of y = f(x). h(x) = f(x) Reflection in the x-axis 2. h(x) = f(x) Reflection in the y-axis

    8. Example 2. Given f(x) = x3 + 3, describe the reflections in the graph of f generated by the following functions. a) g(x) = x3 + 3. b) h(x) = x3 3.

    9. Example 3. Below is the graph of y = f(x). Graph y = f(x). b) Graph y = f(x) + 1

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