Question

What is the equation of the horizontal asymptote of the graph of y = 1/x+5 – 4?

Answer 1

`y=(1)/(x+5)-4`

We can find the horizontal asymptote of this kind of functions using the limit:

`\begin{gathered} \lim _(x\to\infty)(1)/(x+5)-4=(1)/(\infty)-4=-4 \\ \lim _(x\to\infty)(1)/(x+5)-4=(1)/(-\infty)-4=-4 \end{gathered}`

Therefore the equation of the horizontal asymptote is:

`y=-4`