Rational Function Graphs

Which of these functions has an x-intercept at (5,0)?

• $\frac{x+5}{x^2-4}$

• $\frac{x-5}{x^2-7x+10}$

• $\frac{5}{x-5}$

• $\frac{x-5}{x^2+7x+10}$

Given $f\left(x\right)=\frac{x-6}{x^2-36}$  , we would say there is a hole on the graph at...

•  $\left(6,0\right)$  

•  $\left(-6,0\right)$  

•  $\left(6,\frac{1}{12}\right)$  

•  $\left(-6,-\frac{1}{12}\right)$  

• no hole

True or false: the graph of $\frac{2x\left(x-4\right)}{\left(x+7\right)\left(x-1\right)}$  has a horizontal asymptote at y=2

• True

• False

True or False: There is no y-intercept for the graph of: $f\left(x\right)=\frac{5x+2}{x^2+2x}$  

• True

• False

What is/are the vertical asymptote(s) for $f\left(x\right)=\frac{x}{x^2-4x}$  ?

• x=0

• x=0 and x=4

• x=2 and x=-2

• x=4

• There are no vertical asymptotes

What is/are the x-intercept(s) for: $f\left(x\right)=\frac{x^2+8x+15}{x^2+4x-5}$  

• (-3,0) and (-5,0)

• (3,0) and (5,0)

• (-5,0) and (0,1)

• (5,0)

• (-3,0)

What is the y-intercept for $f\left(x\right)=\frac{\left(x-3\right)\left(x-4\right)}{\left(x+1\right)\left(x-2\right)}$  ?

• (0,3) and (4,0)

• (0,-6)

• (0,6)

• (0,7)

• no y-intercept

Choose all of the functions that have a horizontal asymptote at y=1

• $f\left(x\right)=\frac{x^2}{x^2-1}$

• $f\left(x\right)=\frac{x^2+5}{x+5}$

• $f\left(x\right)=\frac{2x\left(x-4\right)}{\left(x+1\right)\left(2x-3\right)}$

• $f\left(x\right)=\frac{3x}{3x^2-3}$

Which of these equations has a y-intercept at $\left(0,\frac{1}{2}\right)$  ?

•  $\frac{x^2+4x+4}{x+2}$  

•  $\frac{3x-5}{x^2-10x}$  

•  $\frac{2\left(x-6\right)}{\left(x-6\right)\left(x-2\right)}$  

•  $\frac{x-3}{\left(x+2\right)\left(x+3\right)}$  

• none of these

Choose all of the functions that have a hole:

•  $f\left(x\right)=\frac{x^2+7x}{x^2-6x-7}$  

•  $f\left(x\right)=\frac{\left(x+8\right)\left(x-2\right)}{\left(x+2\right)\left(x+8\right)}$  

•  $f\left(x\right)=\frac{x-5}{\left(x+5\right)\left(x-1\right)}$  

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

•  $f\left(x\right)=\frac{x^2+3x}{5x}$