# 3.6 Review and Summary

Access this online video resource for additional instruction and practice with transformation of functions.

## Key Equations

 Vertical shift $g\left(x\right)=f\left(x\right)+k\text{}$ (up for $\text{}k>0$) Horizontal shift $g\left(x\right)=f\left(x-h\right)$ (right for $\text{}h>0$) Vertical reflection $g\left(x\right)=-f\left(x\right)$ Horizontal reflection $g\left(x\right)=f\left(-x\right)$ Vertical stretch $g\left(x\right)=af\left(x\right)\text{}$ ($a>0$) Vertical compression $g\left(x\right)=af\left(x\right)\text{}$ ($0 < a < 1$) Horizontal stretch $g\left(x\right)=f\left(bx\right)$ ($0 < b < 1$) Horizontal compression $g\left(x\right)=f\left(bx\right)\text{}$ ($b > 1$)

## Key Terms

• Even Function – a function whose graph is unchanged by horizontal reflection, $\text{}f\left(x\right)=f\left(-x\right)\text{}$, and is symmetric about the $y\text{-}$axis.
• Horizontal Compression – a transformation that compresses a function’s graph horizontally, by multiplying the input by a constant $\text{}b>1$.
• Horizontal Reflection – a transformation that reflects a function’s graph across the y-axis by multiplying the input by $\text{}-1$.
• Horizontal Shift – a transformation that shifts a function’s graph left or right by adding a positive or negative constant to the input.
• Horizontal Stretch – a transformation that stretches a function’s graph horizontally by multiplying the input by a constant $0 < b < 1$.
• Odd Function – a function whose graph is unchanged by combined horizontal and vertical reflection, $f\left(x\right)=-f\left(-x\right)$
• Vertical Compression – a function transformation that compresses the function’s graph vertically by multiplying the output by a constant $0 < a<1$.
• Vertical Reflection – a transformation that reflects a function’s graph across the x-axis by multiplying the output by $\text{}-1$.
• Vertical Shift – a transformation that shifts a function’s graph up or down by adding a positive or negative constant to the output.
• Vertical Stretch – a transformation that stretches a function’s graph vertically by multiplying the output by a constant $\text{}a>1$.