Graphing Polynomial Functions

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Graphing Polynomial Functions

Function Translations

1.  Shift graphs horizontally - right and left

2.  Shift graphs vertically - up and down
3.  Make the graph wider or narrower

Horizontal Shifts

1. Shift the graph right   $f\left(x-c\right)$   moving in the positive direction                 - red graph

2. Shift the graph left   $f\left(x+c\right)$  moving in the negative direction              - blue graph

Poll

The function

$$f\left(x\right)\ =\ 2x^3-7x^2+2x\ -8$$  can be shifted left 2 spaces by which function?

• $$f\left(x-2\right)\ =\ 2x^3-7x^2+2x\ -8$$  

• $$f\left(x+2\right)\ =\ 2x^3-7x^2+2x\ -8$$  

• $$f\left(x\right)-2\ =\ 2x^3-7x^2+2x\ -8$$  

• $$f\left(x\right)+2\ =\ 2x^3-7x^2+2x\ -8$$  

Vertical Shifts

1. Shift the graph up   $f\left(x\right)+c$ moving the graph up           example  $y=x^2+4$  

2.  Shift the graph down   $f\left(x\right)-c$   moving the graph down      example  $y=x^2-3$  

Poll

The function

$$f\left(x\right)\ =\ 2x^3-7x^2+2x\ -8$$  can be shifted down 2 spaces by which function?

• $$f\left(x-2\right)\ =\ 2x^3-7x^2+2x\ -8$$  

• $$f\left(x+2\right)\ =\ 2x^3-7x^2+2x\ -8$$  

• $$f\left(x\right)-2\ =\ 2x^3-7x^2+2x\ -8$$  

• $$f\left(x\right)+2\ =\ 2x^3-7x^2+2x\ -8$$  

Changing the Width

Making the graph wider or narrower    $cf\left(x\right)$   or    $f\left(cx\right)$  

Poll

The function

$$f\left(x\right)\ =\ 2x^3-7x^2+2x\ -8$$  is dilated by a factor of 2 by which function?

• $$f\left(x-2\right)\ =\ 2x^3-7x^2+2x\ -8$$  

• $$f\left(x+2\right)\ =\ 2x^3-7x^2+2x\ -8$$  

• $$f\left(x\right)-2\ =\ 2x^3-7x^2+2x\ -8$$  

• $$2f\left(x\right)\ =\ 2x^3-7x^2+2x\ -8$$