Parent Functions & Transformations

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Presentation transcript:

Parent Functions & Transformations

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

Graph the parent function using a table of values 1.

Graph the parent function using a table of values 2.

Graph the parent function using a table of values 3.

Graph the parent function using a table of values 4.

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

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

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

Graph the function 5.

Graph the function 6.

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

Graph the function 7.

Graph the function 8.

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

Graph the function 9.

Graph the function 10.

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

Graph the function 11.

Graph the function 12.

Graph the function 13.

Graph the function 14.