Key Features of Functions and Transformations of Functions

Given the functions  $f\left(x\right)=\ -3\left(x\ +\ 4\right)^{2\ }+6$  identify the domain 

•  $\left(\infty,-\infty\right)$  

•  $\left(-\infty,\infty\right)$  

•  $\left(-\infty,\ 6\right]$  

•  $\left(\infty,\ 6\right]$  

Given the functions  $f\left(x\right)=\ \left|x-9\right|+2$  identify the range

•  $\left(-\infty,2\right]$  

•  $\left(-\infty,2\right)$  

•  $\left[2,\infty\right]$  

•  $\left[2,\infty\right)$  

Given the functions  $f\left(x\right)=\ -3\left(x\ +\ 4\right)^{2\ }+6$  identify the intervals of increase

•  $\left(-\infty,-4\right)$  

•  $\left(\infty,-4\right)$  

•  $\left(-\infty,\ 6\right)$  

•  $\left(\infty,\ 6\right)$  

Given the functions  $f\left(x\right)=\ -3\left(x\ +\ 4\right)^{2\ }+6$  identify the intervals of decrease

•  $\left(-4,-\infty\right)$  

•  $\left(-4\ ,\ \infty\right)$  

•  $\left(6,-\infty\right)$  

•  $\left(6,\infty\right)$  

Given the functions  $f\left(x\right)=\ -3\left(x\ +\ 4\right)^{2\ }+6$  identify the end behavior

•  $x\rightarrow-\infty,\ f\left(x\right)\rightarrow\ -\infty\$   $x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$  

•  $x\rightarrow-\infty,\ f\left(x\right)\rightarrow+\infty$   $\ \ \ x\rightarrow+\infty,\ f\left(x\right)\rightarrow\ +\infty$  

•  $x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$   $x\rightarrow-\infty,\ f\left(x\right)\rightarrow\ +\infty\$  

•  $x\rightarrow-\infty,\ f\left(x\right)\rightarrow-\infty\ \ \ \ \$   $x\rightarrow+\infty,\ f\left(x\right)\rightarrow-\infty$  

Given the functions  $f\left(x\right)=\ \left|x-9\right|+2$  identify the intervals of Increase

•  $\left(9,\infty\right)$  

•  $\left(-\infty,2\right)$  

•  $\left(-\infty,\ 9\right)$  

•  $\left(\infty,\ 9\right)$  

Given the functions  $f\left(x\right)=\ -3\left(x\ +\ 4\right)^{2\ }+6$  identify the function type

• Rational

• Absolute Value

• Quadratic 

• Square Root

Given the functions  $f\left(x\right)=\ -3\left(x\ +\ 4\right)^{2\ }+6$  identify the Key Feature

• Asymptotes: VA: X = -4 ; HA: y = 6 

• Vertex: (-4.6)

• Starting Point: (-4,6)

Given the functions  $f\left(x\right)=\ \left|x-9\right|+2$  identify the function type

• Rational

• Absolute Value

• Quadratic 

• Square Root

Given the functions  $f\left(x\right)=\ \frac{3}{x+6}-8$  identify the function type

• Rational

• Absolute Value

• Quadratic 

• Square Root