Transformations of Functions Review

Horizontal translation left

Vertical shrink

Vertical translation down

Horizontal translation right

Vertical stretch

$y=x^2$

$y=x^3$

$y=\left|x\right|$

$y=\frac{1}{x}$

$y=2\left(x-5\right)^2+4$

$y=2\left(x+5\right)^2+4$

$y=-2\left(x-5\right)^2+4$

$y=-2\left(x+5\right)^2+4$

$f\left(x\right)=-\sqrt{x+4}-2$

$f\left(x\right)=\sqrt{x-4}-2$

$f\left(x\right)=-\sqrt{x-4}-2$

$f\left(x\right)=\sqrt{x+4}+2$

Vertical compression by ⅓ and left 9

Vertical compression ⅓ and right 9

Horizontal stretch by 3 and left 9

Horizontal stretch by 3 and right 9

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

$f\left(x\right)\ =\ 7\left|-x\right|$

$f\left(x\right)\ =\ \sqrt{-7x}$

$f\left(x\right)\ =\ -\left|7x\right|$

$f\left(x\right)\ =\ \left|x+4\right|+7$

$f\left(x\right)\ =\ \left(x-4\right)^2\ +\ 7$

$f\left(x\right)\ =\ \left(x+7\right)^2-\ 4$

$f\left(x\right)\ =\ \left|x+4\right|-7$

Vertically compressed by 2, Reflected over y-axis, Right 5

Vertically stretched by 2, Reflected over x-axis, Left 5

Vertically stretched by 2, Reflected over x-axis, Right 5

Vertically compressed by 2, reflected over y-axis, Left 5

Linear

Absolute Value

Quadratic

Square Root

shifted up five units

reflection in x-axis

shifted down five units

reflection in x-axis

shifted left 5 units

reflection x-axis

shifted right 5 units

reflection x-axis