Algebra 2 Review of Functions Part 2 Notes

Parent Function:  $y=x^3$  

Domain:  All Real Numbers

Range:  All Real Numbers

Transformation Equation:   $y=a\left(x-h\right)^3+k$  

a: reflect, stretch, compress

h: moves left or right

k: moves up or down

Parent Function:  $y=^3\sqrt{x}$  

Domain:  All Real Numbers

Range: All Real Numbers

Transformation Equation:  $y=a\ ^3\sqrt{x-h}+k$  

a: reflect, stretch, compress

h: moves left or right

k: moves up and down

No parent function

Example:   $y=2^x$  

Domain: All Real Numbers

Range: y > 0

Asymptote: y = 0

Transformation Equation:  $y=a\cdot2^{\ x-h}+k$  

No parent function

Example:   $y=\left(\frac{1}{2}\right)^x$  

Domain: All Real Numbers

Range: y > 0

Asymptote: y = 0

Transformation Equation:  $y=a\cdot\left(\frac{1}{2}\right)^{\ x-h}+k$  

y = log (x)

Domain: x > 0

Range: All Real Numbers

Asymptote: x = 0

Transformation Equation:  $y=a\ \log\left(x-h\right)+k$  

Parent Function:  $y=\frac{1}{x}$  

Domain:  $x\ne0$  

Range:  $y\ne0$  

Vertical Asymptote: x = 0

Horizontal Asymptote: y = 0

Transformation Equation:  $y=\frac{a}{x-h}+k$