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

EXPLANATION

The given equation is

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

The vertical asymptote is determined by equating the denominator to zero and solve for x.

$x + 4 = 0$

The equation of the vertical asymptote is

$x = - 4$

The numerator has the same degree as the denominator.

The equation of the horizontal asymptote is the coefficient of the leading term in the numerator expressed over the coefficient of the leading term in the denominator.

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

y=2