Question

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

Answer 1

Option C: $x=-4$ , $y=2$ is the asymptotes of the equation.

Explanation:

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

The vertical asymptote of the equation can be determined by equating the denominator of the equation to zero.

Thus, we have,

$x+4=0$

      $x=-4$

Hence, the vertical asymptote of the function is $x=-4$

Now, we shall determine the horizontal asymptote.

The horizontal asymptote of the function can be determined by dividing the leading coefficient of x in the numerator by the leading coefficient of x in the denominator.

Thus, we have,

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

$y=2$

Hence, the horizontal asymptote of the function is $y=2$

Therefore, Option C is the correct answer.