Precal GL Ch 2-5 Graphing Rational Functions

What is the y-intercept of the function  $f\left(x\right)=\frac{2x-12}{x+3}$  ?

• (0,2)

• (0,-3)

• (0,6)

• (0,-4)

What is the x-intercept of the function  $y=\frac{2x-12}{x+3}$  ?

• (2,0)

• (-3,0)

• (6,0)

• (-4,0)

How many vertical asymptotes does the function  $\frac{x^2+4x-12}{2x^2+13x+6}=f\left(x\right)$  have?

• 1

• 2

• None because of the hiatus point

• None due to having a slant asymptote

Given  $y=\frac{x^2+4x-12}{2x^2+13x+6}$  :  What is the hiatus point?

• There isn't one.

•  $\left(-6,6\right)$  

•  $\left(-6,\ \frac{8}{11}\right)$  

•  $\left(6,\frac{4}{13}\right)$  

What causes a slant asymptote in a rational function?

• If the numerator has no variable x in it

• If the numerator is one degree smaller than the denominator

• If the numerator and denominator are of equal degree

• If the numerator is one degree higher than the denominator

Find the vertical asymptote(s) of the function  $f\left(x\right)=\frac{-23}{x^2+8x+7}$  .

•  $y=0$  

•  $x=7,\ x=1$  

•  $x=-7,\ x=-1$  

•  $x=-23$  

What is the slanted asymptote of the function  $y=\frac{-26+11x+x^2}{x^2-5+4x}$  ?

•  $x=-13,\ x=2$  

• There isn't one.

•  $x=-5,\ x=1$  

•  $y=1$  

What happens at  $x=-6$  in the function $\frac{x+2}{\left(x+6\right)^2}$  ?

• There is a hiatus point.

• Both branches of the graph go down to  $-\infty$  .

• There is no horizontal asymptote.

• Both branches of the graph go up to  $\infty$  .

What is the hiatus point of the function  $y=\frac{x^2+5x-6}{x^2+4x-5}$  ?

•  $\left(-1,\frac{5}{4}\right)$  

• There isn't one.

•  $\left(0,0\right)$  

•  $\left(1,\frac{7}{6}\right)$  

What are the vertical and horizontal asymptotes of the function shown?

• x = -1, y = -3

• x = 1, y = -3

• x = -1, y = 3

• x = 1, y = 3