Question

Which is a graph of f(x)=5x-2/x+2,with any vertical or horizontal asymptotes indicated by dashed lines?

Answer 1

Answer:

The graph of the given function f(x) is attached below :

$f(x)=\frac{5\cdot x -2}{x+2}$

To find vertical asymptotes :

Since the given function is rational so the vertical asymptotes of the function will be zeroes of the denominator

Vertical Asymptotes : x + 2 = 0

⇒ x = -2

To find horizontal asymptotes :

As the degree of numerator is s equal to the degree of denominator. Therefore,

$\text{Horizontal asymptote, y = }\frac{\text{Numerator's leading coefficient}}{\text{Denominator's leading coeeficient}}\\\\\bf\implies y = \frac{5}{1}=5$