Algebra 2 Review of Functions Part 2 Notes

Algebra 2 Review of Functions Part 2

Cubic Functions

• Parent Function:  $y=x^3$  

• Domain:  All Real Numbers

• Range:  All Real Numbers

Cubic Functions

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

• a: reflect, stretch, compress

• h: moves left or right

• k: moves up or down

Cube Root Functions

• Parent Function:  $y=^3\sqrt{x}$  

• Domain:  All Real Numbers

• Range: All Real Numbers

Cube Root Functions

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

• a: reflect, stretch, compress

• h: moves left or right

• k: moves up and down

The Cubic and Cube Root Functions are Inverses of One Another

Exponential Growth

• No parent function

• Example:   $y=2^x$  

• Domain: All Real Numbers

• Range: y > 0

• Asymptote: y = 0

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

Exponential Decay

• No parent function

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

• Domain: All Real Numbers

• Range: y > 0

• Asymptote: y = 0

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

Logarithmic Functions

• y = log (x)

• Domain: x > 0

• Range: All Real Numbers

• Asymptote: x = 0

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

Rational Functions

• Parent Function:  $y=\frac{1}{x}$  

• Domain:  $x\ne0$  

• Range:  $y\ne0$  

• Vertical Asymptote: x = 0

• Horizontal Asymptote: y = 0

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