2B Review Core (Rational Functions and Non-Linear Inequalities)

(Check all that apply) Give the equation of the vertical asymptote(s) of

 $f\left(x\right)=\frac{1}{x+3}$ 

• x = -3

• x = 3

• none

• x = 1

• x = 0

(Check all that apply) Give the equation of the vertical asymptote(s) of

 $f\left(x\right)=\frac{-1}{x^2-4}$ 

• x = 4

• x = 2

• none

• x = -1

• x = -2

(Check all that apply) Give the equation of the vertical asymptote(s) of

 $f\left(x\right)=\frac{1}{x^2-5x-36}$ 

• x = -4

• x = 9

• none

• x = -9

• x = 4

Give the domain of

 $f\left(x\right)=\frac{1}{x^2-5x-36}$ 

• (-∞,-4)U(-4,9)U(9,∞)

• (-∞,-9)U(-9,4)U(4,∞)

• (-∞,∞)

• (-9,4)

• (-4,9)

(Check all that apply) State the x-values where there is a discontinuity. Label them as removable or non-removable.

 $f\left(x\right)=\frac{2x-14}{3x\left(x-7\right)}$  

• x = 7, removable

• x = 7, non-removable

• x = 0, removable

• x = 0, non-removable

• x = 3, non-removable

(Check all that apply) Find the x- and y-intercepts of f(x) as ordered pairs.

 $f\left(x\right)=\frac{x^2-2x-15}{x+5}$  

• (0,-3)

• (-3,0)

• (5,0)

• (-5,0)

• (3,0)

Find the end behavior asymptote of f(x).

 $f\left(x\right)=\frac{x^2-2x-15}{x+5}$  

• y = x - 7

• y = x + 3

• y = 0

• y = 1

• y = -2

Find the end behavior asymptote of f(x).

 $f\left(x\right)=\frac{2x^2-1}{x^2+3}$  

• y = 2x - 6

• y = 2x - 7

• y = 0

• y = 1

• y = 2

Find the end behavior limits of

 $f\left(x\right)=\frac{-8}{x^2-4}$  

•  $\lim_{x\rightarrow\pm∞}f\left(x\right)=0$  

•  $\lim_{x\rightarrow\pm∞}f\left(x\right)=-8$  

•  $\lim_{x\rightarrow\pm∞}f\left(x\right)=2$  

•  $\lim_{x\rightarrow-∞}f\left(x\right)=-∞\ ;\ \lim_{x\rightarrow∞}f\left(x\right)=∞$  

•  $\lim_{x\rightarrow-∞}f\left(x\right)=∞\ ;\ \lim_{x\rightarrow∞}f\left(x\right)=-∞$  

Find the end behavior asymptote of f(x).

 $f\left(x\right)=\frac{x^3-2x^2-3x-4}{x-2}$  

•  $y=x^2-3$  
  

•  $y=x^2-4x+5$  

• y = 0

• y = 1

• y = 2