Dominant Terms & Limits of Rational Functions

Find the limit.

• 0

• $\frac{8}{17}$

• $-\infty$

• $\infty$

Identify the equation of the horizontal asymptote (y=__) for the given function.

Find the limit.

Identify the equation of the horizontal asymptote (y=__) for the given function.

Find the limit of the given function.

• 0

• $\infty$

• $-\infty$

• $\frac{4}{5}$

Find the limit of the given function.

Identify the equation of the horizontal asymptote.

• $y=\frac{4}{9}$

• $y=0$

• none

Identify the equation of the horizontal asymptote.

• $y=0$

• $y=-\frac{1}{4}$

• none

Find the limit.

Identify the coordinates of the hole and equations of the asymptotes.

 $f\left(x\right)=\frac{3x-1}{x-4}$  

• No Holes;  No Horizontal Asymptote;  VA:  x = 4

• No Holes;  HA: y = 3;  VA:  x = 4

• Hole @ x = 4;  No Horizontal Asymptote;  VA @ x =  $\frac{1}{3}$  

• Hole @ x = 4;  HA: y = 3;  No Vertical Asymptote