Polynomial and Rational Unit Review

Find the end behavior of  $f\left(x\right)=-2x^3+5x^4$  .

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=+\infty$  and  $\lim_{x\rightarrow+\infty}f\left(x\right)=-\infty$  

•  $\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty$   and  $\lim_{x\rightarrow+\infty}f\left(x\right)=+\infty$  

•   $\lim_{x\rightarrow\pm\infty}f\left(x\right)=-\infty$  

•  $\lim_{x\rightarrow\pm\infty}f\left(x\right)=+\infty$  

The graph below is the graph of g(x). Write g(x) as a product of linear factors.

• $g\left(x\right)=x\left(x+3\right)\left(x-1\right)$

• $g\left(x\right)=x\left(x-3\right)\left(x+1\right)$

• $g\left(x\right)=\left(x+3\right)\left(x-1\right)$

• $g\left(x\right)=\left(x-3\right)\left(x+1\right)$

Tags

CCSS.HSA.APR.B.3

 $f\left(x\right)=x^5-10x^2-x+10.\ \ \$  Which of the following is not a root of f(x)?

•  $-1+2i$  

•  $1+2i$  

•  $-1$  

•  $1$  

For which of the following values of k will  $g\left(x\right)=\frac{kx+6}{4x-5}$  have an end behavior of  $\lim_{x\rightarrow\pm\infty}g\left(x\right)=3$  ?

• k = 18

• k = 12

• k = 2

• k = 3

Tags

CCSS.HSF-IF.C.7D

Which of the following occurs in the graph of  $y=\frac{2x^2-8}{x-2}$  at x = 2?

• A vertical asymptote at x = 2

• The defined point (2, 4)

• A point of discontinuity at (2, 0)

• A point of discontinuity at (2, 8)

Tags

CCSS.HSF-IF.C.7D

Find the equations of the vertical asymptotes of $y=\frac{x\left(x-1\right)}{x^2+2x-3}$  .

•  $x=-3$  and $x=1$  

•  $x=-3$  only

•  $x=3$  and  $x=-1$  

•  $x=3$  only

Tags

CCSS.HSF-IF.C.7D

Find the domain of $y=\frac{x-4}{x^2-4}$ .

•  $\left(-\infty,\ 0\right)\cup\left(0,\ +\infty\right)$  

•  $\left(-\infty,\ 4\right)\cup\left(4,\ +\infty\right)$  

•  $\left(-\infty,\ -2\right)\cup\left(-2,\ 2\right)\cup\left(2,\ +\infty\right)$  

•  $\left(-\infty,\ 2\right)\ \cup\ \left(2,\ +\infty\right)$  

What is the equation of the slant asymptote of the function $h\left(x\right)=\frac{x^2+9x+28}{x+5}$  ?

•  $y=x-5$  

•  $y=x+4$  

•  $y=x+3$  

•  $y=x-4$  

Tags

CCSS.HSF-IF.C.7D

Factor and solve:
14=2x²- 12x

• x=7,1
• x=-7,1
• x=-1,7
• No solution

Tags

CCSS.HSA-REI.B.4B

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

• y = ^_(x + 2)(x - 1)²

• y = -(x - 2)(x + 1)²

• y = (x - 2)(x + 1)²

• y = -x³