Question

Determine the equations of the vertical and horizontal asymptotes, if any, for f(x)=2x/x+4

Answer 1

Answer:

Vertical asymptote:x=-4

Horizontal asymptote: y=2

Step-by-step explanation:

The given rational function is

$f(x)=\frac{2x}{x+4}$

To find the vertical asymptote we equate the denominator to zero and solve for x.

x+4=0

The equation of the vertical asymptote is

x=-4

To find the horizontal asymptote we take limit to infinity. Or simply express the coefficient of x in the numerator over the coefficient of x in the denominator since this is a proper rational function.

The horizontal asymptote has equation

$y=\frac{2}{1} =2$