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Published byKasandra Spire Modified about 1 year ago

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PARENT FUNCTIONS & TRANSFORMATIONS

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Parent functions are common functions of algebra that we. A is when we, or a graph. The graph maintains the same general characteristics, but it morphed. transform transformation shiftreflect stretch/compress

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Graph the parent function using a table of values 1.

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Graph the parent function using a table of values 2.

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Graph the parent function using a table of values 3.

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Graph the parent function using a table of values 4.

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A is a slide. When we graph translations, we will the graph from one location to another. translation shift

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Vertical Shifts A shift moves the graph or. If is our function, the graph of is the graph of shifted c units vertically upward. If is our function, the graph of is the graph of shifted c units vertically downward. Note: with vertical shifts, the sign on the movement (+/-) is the direction as what the shift is. So, if the sign is positive we go and when the sign is negative we go. Vertical shifts are never the parentheses. verticalup down same up down inside

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When looking at the equation of a parent function, a vertical shift is grouped with the x. not

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Graph the function 5.

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Graph the function 6.

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Horizontal Shifts A shift moves the graph or. If is our function, the graph of is the graph of shifted c units horizontally to the left. If is our function, the graph of is the graph of shifted c units horizontally to the right. Note: with horizontal shifts, the sign on the movement (+/-) is the direction as what the shift is. So, if the sign is positive we go and when the sign is negative we go. Horizontal shifts are inside the parentheses. horizontal left right opposite left right always

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Graph the function 7.

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Graph the function 8.

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Vertical Reflections A reflection is a reflection about the. The graph of is the graph of reflected about the x-axis. In other words, if there is a out front, we flip over the. vertical x-axis negative x-axis

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Graph the function 9.

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Graph the function 10.

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Combining Shifts and Reflections We can graph both a vertical and horizontal shift at the same time. Just remember the vertical movement is the parentheses, and the horizontal movement is the parentheses. A vertical reflection will also be the parentheses. Order of transformations – work from the inside out! Horizontal Shift Vertical Reflection Vertical Shift outside inside outside

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Graph the function 11.

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Graph the function 12.

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Graph the function 13.

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Graph the function 14.

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