Transformations Pre Calc

Addition or subtraction outside the parentheses

Vertical translations

Addition or subtraction inside the parentheses

Horizontal translation

Important things to remember about horizontal translations

Adding: shifts left

Subtracting: shifts right

Multiplying outside parentheses and a is greater than 0

Dilated by factor of a

Greater than 1: graph gets skinnier

Fraction: graph gets wider

Multiplying inside parentheses

Graph always shrinks/ gets skinnier

Multiplying by a negative outside the parentheses

Graph reflects over the x axis

Multiplying by a negative inside the parentheses

Graph reflects over the y axis

f(x)=x

Line

f(x)=|x|

V shaped graph

f(x)=x²

U shaped graph

f(x)=x³

Squiggly s graph

f(x)=\sqrt{x}

Straw shaped graph

f(x)=1/x

Two bent lines graph