Quiz Graphing Rational Functions

What is the horizontal asymptote of f(x)=(3x²+7)/(x²-2x-3)?

• y=⅓

• y=0

• None

• y=3

What are the vertical asymptotes of f(x)=(x²+3)/(x²+x-6)?

• x=3, x=-2

• x=3, x=2

• x=-3, x=-2

• x=-3, x=2

How do you find the x intercepts of a rational function?

• Find the zeros of the denominator.

• Compare the power of the numerator to the power of the denominator.

• Find the zeros of the numerator.

• Find the lead coefficient of the numerator over the lead coefficient of the denominator.

What are the asymptotes?

• x=1, x= 2, y =1, y= 2
• x= 2, x=-2, y = 1
• x=2 y =-1
• x=1 y =2, y =-2

Match the graph to the correct rational equation below.

• f(x)=x²/(x²+x-12)

• f(x)=4x²/(x²-x-12)

• f(x)=(2x²-2)/2x²

• f(x)=x/(x²+x-12)

What is the y-intercept for this rational function?

• $\left(0,\ 4\right)$

• $\left(0,\ \frac{1}{4}\right)$

• $\left(0,\ -\frac{3}{2}\right)$

• $\left(0,\ 6\right)$

Which of the following is the graph of the function:

 $f\left(x\right)=\frac{2}{x+1}+1$  

• 
• 
• 
• 

What is the domain and range of f(x)=(2x+5)/(x+3)?

• Domain: (-∞,-3)U(-3,∞) Range: (-∞,2)U(2,∞)

• Domain: (-∞,2)U(2,∞) Range: (-∞,-3)U(-3,∞)

• Domain: (-∞,-½)U(-½,∞) Range: (-∞,2)U(2,∞)

• Domain: (-∞,-3)U(-3,∞) Range: (-∞,4)U(4,∞)

Determine the hole(s) of the function.

 $f\left(x\right)=\frac{5x-10}{x^2-4}$  

•  $\left(2,\ \frac{5}{4}\right)$  
  

• None

•  $\left(-2,\ \frac{3}{4}\right)$  
  

•  $\left(2,\ 0\right)$  
  

Determine the range of the function.

 $f\left(x\right)=\frac{x^2+4x-32}{x^2-5x+4}$  

• Range:  $y\ne1,\ 4$  

• Range:  $y\ne-8$  

• Range: All Real Numbers

• Range:  $y\ne0,-2$