Pre-Calculus Unit 2 Review

 What is happening on the graph of the polynomial function

 $y=4x^{3\ }-12x^2+9x$  at  $x=\frac{3}{2}$  ?

• There is an x-intercept that "crosses" the x-axis.

• There is an x-intercept that "bounces off" the x-axis.

• There is not an x-intercept at this x-value.

 What is happening on the graph of the polynomial function

 $y=4x^{3\ }-12x^2+9x$  at  $x=0$  ?

• There is an x-intercept that "crosses" the x-axis.

• There is an x-intercept that "bounces off" the x-axis.

• There is not an x-intercept at this x-value.

What is the end behavior of the graph of the polynomial function $f\left(x\right)=6+7x-x^3$  ?  (Choose 2)

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

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

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

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

What is the value of the remainder when you divide the polynomial function $f\left(x\right)=3x^4-6x^2+3x-1$  by  $x+2$  ? (Choose all that apply.)

• 17

• 29

• -7

•  $f\left(-2\right)$  

•  $f\left(2\right)$  

Which of the following is a full list of the possible rational zeros for the polynomial function $f\left(x\right)=4x^3+3x^2-3+6$  ?

•  $\pm\frac{1}{4},\pm\frac{1}{2},\pm\frac{3}{4},\pm1,\pm1\ \frac{1}{2},\ \pm2,\ \pm3,\ \pm6$  

•  $\pm\frac{1}{6},\pm\frac{1}{3},\pm\frac{1}{2},\pm\frac{2}{3},\pm1,\ \pm1\ \frac{1}{3},\ \pm2,\ \pm4$  

•  $\pm1,\ \pm2,\ \pm3,\ \pm6$  

•  $\pm1,\ \pm2,\ \pm3,\ \pm4,\ \pm6$  

Find the rational zeros of the function  $f\left(x\right)=3x^5+2x^4-3x-2$ .  (Choose all that apply.)

•  $x=1$  

•  $x=-1$  

•  $x=-\frac{2}{3}$  

•  $x=\frac{2}{3}$  

•  $x=\pm i$  

The solutions of the quadratic equation $x^2-2x+8=0$  are  $x=?\pm i\sqrt{7}$  . (Find the missing "?" value in the solutions.)

Write the function  $f\left(x\right)=x^3-7x^2+11x+19$ as a product of linear factors.  Select its linear factors from the list below.

•  $\left(x+1\right)$  

•  $\left(x-1\right)$  

•  $\left(x-4\pm i\sqrt{3}\right)$  

•  $\left(x\pm4-i\sqrt{3}\right)$  

•  $\left(x+4\pm i\sqrt{3}\right)$  

Find the vertical asymptote(s) of the rational function $f\left(x\right)=\frac{2x+12}{x^2-36}$  .

•  $x=6$  

•  $x=6$  and  $x=-6$  

•  $x=0$  

•  $x=2$  

• It does not have any vertical asymptotes.

Find the horizontal asymptote of the rational function $f\left(x\right)=\frac{2x+12}{x^2-36}$  .

•  $y=0$  

•  $y=2$  
  

•  $y=6$  

•  $y=-6$  

• It does not have a horizontal asymptote.