Analyzing Rational Functions: (3 Examples)

Find the x-intercept of this function.

• (-5,0)

•  $\left(-\frac{1}{7},0\right)$  

• (5,0)

• It does not have an x-intercept.

Find the y-intercept of this function.

• (0,-5)

•  $\left(0,-\frac{1}{7}\right)$  

• (0,5)

• It does not have an x-intercept.

Find the vertical asymptote of this function.

• x=-5, x=7

• x=-5

• x=7

• It does not have a vertical asymptote.

Find the horizontal asymptote of this function.

• y=0

• y=1

•  $y=\frac{1}{2}$  
  

• It does not have a horizontal asymptote.

Find the coordinates of the hole of this function.

• (-5,0)

•  $\left(5,\frac{1}{2}\right)$  

•  $\left(-5,-\frac{1}{12}\right)$  
  

• It does not have a hole.

Find the x-intercept of this function.

• (-4,0)

• (3,0)

• (-4,0) & (3,0)

• There is no x-intercept.

Find the y-intercept of this function.

• (0,-4)

• (0,2)

• (0,-2)

• There is no y-intercept.

Find the vertical asymptote of this function.

• x=3

• x=-2

• x=3, x=-2

• There is no vertical asymptote.

Find the horizontal asymptote of this function.

• y=0

• y=1

• y=2

• There is no horizontal asymptote.

Find the hole of this function.

• y=0

• y=1

• $\left(3,\frac{7}{5}\right)$

• There is no horizontal asymptote.