Graphing Polynomial Functions

Presentation

•

Mathematics

•

9th - 12th Grade

•

Easy

•

CCSS

HSF.BF.B.3

Standards-aligned

Keh Ivy

Used 14+ times

FREE Resource

5 Slides • 3 Questions

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?

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

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

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

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

Graphing Polynomial Functions

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