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

Sagot :

[tex]y=\frac{1}{x+5}-4[/tex]

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

[tex]\begin{gathered} \lim _{x\to\infty}\frac{1}{x+5}-4=\frac{1}{\infty}-4=-4 \\ \lim _{x\to\infty}\frac{1}{x+5}-4=\frac{1}{-\infty}-4=-4 \end{gathered}[/tex]

Therefore the equation of the horizontal asymptote is:

[tex]y=-4[/tex]

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