HW Transformations and End Behavior

Determine the PARENT FUNCTION of the following function:

 $f\left(x\right)=3\left(x-2\right)^{12}-8$  

•  $y=x^{12}$  

•  $y=3x^{11}$  

•  $y=x^{13}$  

•  $y=x^3$  

Determine the HORIZONTAL movement of the following function:

 $f\left(x\right)=3\left(x-2\right)^{12}-8$  

• 2 right

• 2 left 

•  8 right

• 8 left 

Determine the VERTICAL movement of the following function:

 $f\left(x\right)=3\left(x-2\right)^{12}-8$  

• 2 up

• 2 down 

•  8 up

• 8 down 

Determine the PARENT FUNCTION of the following function:

 $f\left(x\right)=-\frac{1}{2}\left(x+6\right)^9+13$  

•  $y=x^9$  

•  $y=-\frac{1}{2}x^8$  

•  $y=x^{10}$  

•  $y=x^{-\frac{1}{2}}$  

Determine the HORIZONTAL movement of the following function:

 $f\left(x\right)=-\frac{1}{2}\left(x+6\right)^9+13$  

• 6 right

• 6 left 

• 13 left 

• 13 right 

Determine the VERTICAL movement of the following function:

 $f\left(x\right)=-\frac{1}{2}\left(x+6\right)^9+13$  

• 13 up

• 13 down 

• 6 down 

• 6 up

END BEHAVIOR means what happens at a maximum or a minimum of a polynomial.

• TRUE

• FALSE

Determine the RIGHT END behavior of the function:

 $g\left(x\right)=11x^3-x^2-9x+5$  

•  $\lim_{x\rightarrow\infty}=\infty$  

•  $\lim_{x\rightarrow\infty}=-\infty$  

•  $\lim_{x\rightarrow-\infty}=-\infty$  

•  $\lim_{x\rightarrow-\infty}=\infty$  

Determine the RIGHT END behavior of the function:

 $f\left(x\right)=-2x^5-11x^3+9x+10$  

•  $\lim_{x\rightarrow\infty}=\infty$  

•  $\lim_{x\rightarrow\infty}=-\infty$  

•  $\lim_{x\rightarrow-\infty}=-\infty$  

•  $\lim_{x\rightarrow-\infty}=\infty$  

Determine the LEFT END behavior of the function:

 $g\left(x\right)=11x^3-x^2-9x+5$  

•  $\lim_{x\rightarrow\infty}=\infty$  

•  $\lim_{x\rightarrow\infty}=-\infty$  

•  $\lim_{x\rightarrow-\infty}=-\infty$  

•  $\lim_{x\rightarrow-\infty}=\infty$