Question

Write the equations of the horizontal asymptote and vertical asymptote of the graph

Answer 1

To calculate the vertical asymptotes, we first need to simplify the factors of the radical equation. The equation is already simplified, so we can skip this step.

Next, we need to check which values of x are undefined. Since we can't divide by 0, the vlues for which x makes the denominator equal to zeroare undefined:

`\begin{gathered} x+6=0 \\ x=-6 \end{gathered}`

So, the equation is undefined for x = -6, which means that the equation for the only vertical asymptote is:

`x=-6`

To find the horizontal asymptote, we need to check the degrees of the numerator and the denominator. Both of them are of first degree. When both have the same degree, we calculate the horizontal asymptote by calculating the ratio between their leading coefficients.

The leading coefficient of the numerator is 3 and of the denominator is 1, so the horizontal asympttote is:

`y=(3)/(1)=3`

So, the equation for the horizontal asymptote is:

`y=3`