Rational Functions

To find the domain and vertical asymptotes, you set the bottom of the function equal to zero.

• TRUE

• FALSE

Answer explanation

For the domain, we take the values out of all real numbers, and you just use them with "x=" for the vertical asymptotes

Find the vertical asymptotes of the function:

 $f\left(x\right)=\frac{2x^2+4x-6}{x^2-5x+6}$  

•  $x=2,3$  

•  $x=-3,-2$  

•  $x=-3,1$  

• None

Find the horizontal asymptote of the function:

 $f\left(x\right)=\frac{2x^2+4x-6}{x^2-5x+6}$  

•  $y=2$  

•  $y=0$  

•  $y=-2$  

• None

To find the x-intercepts, you set the bottom equal to zero.

• TRUE

• FALSE

Answer explanation

To find the x-intercepts, you set the TOP equal to zero.

Find the x-intercepts of the function:

 $f\left(x\right)=\frac{2x^2+4x-6}{x^2-5x+6}$  

•  $-3,1$  

•  $2,3$  

•  $-1,3$  

•  $-1$  

To find the y-intercept, you make all the x's equal to zero and simplify.

• TRUE

• FALSE

Answer explanation

This means all you need to do is look at the constant value on top and the constant value on the bottom and divide them.

Find the y-intercept of the function:

 $f\left(x\right)=\frac{2x^2+4x-6}{x^2-5x+6}$  

•  $-1$  

•  $-3$  

•  $1$  

•  $-3,1$  

Find the domain of the function:

 $f\left(x\right)=\frac{x^3-27}{x^2+10x+9}$  

•  $D:\ \ all\ Real\ numbers,\ x\ne-9,-1$  

•  $D:\ \ all\ Real\ numbers,\ x\ne1,9$  

•  $D:\ \ all\ Real\ numbers,\ x\ne3$  

•  $D:\ \ all\ Real\ numbers,\ x\ne-3$  

Find the vertical asymptotes of the function:

 $f\left(x\right)=\frac{x^3-27}{x^2+10x+9}$  

•  $x=-9,-1$  

•  $x=1,9$  

•  $x=3$  

• None

Find the horizontal asymptote of the function:

 $f\left(x\right)=\frac{x^3-27}{x^2+10x+9}$  

•  $y=3$  

•  $y=0$  

•  $y=-3$  

• None