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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 stretch/compress shift reflect

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**Graph the parent function using a table of values**

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**Graph the parent function using a table of values**

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**Graph the parent function using a table of values**

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**Graph the parent function using a table of values**

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**A. is a slide. When we graph translations, we will**

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 vertical up down same up down inside**

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. down same up down inside

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**When looking at the equation of a parent function, a vertical shift is**

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 horizontal left right opposite left right always**

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. 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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1. Transformations To graph: Identify parent function and adjust key points. Function To Graph: Move key point (x,y) to: Vertical Shift up Vertical Shift.

1. Transformations To graph: Identify parent function and adjust key points. Function To Graph: Move key point (x,y) to: Vertical Shift up Vertical Shift.

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