How do I find the horizontal asymptote of 1/(x+7)+3? Show work please.

Question

jim_thompson5910 · Answer

$$\Large \frac{1}{x+7}+3$$

$$\Large \frac{1}{x+7}+3*\frac{x+7}{x+7}$$

$$\Large \frac{1}{x+7}+\frac{3(x+7)}{x+7}$$

$$\Large \frac{1}{x+7}+\frac{3x+21}{x+7}$$

$$\Large \frac{1+3x+21}{x+7}$$

$$\Large \frac{3x+22}{x+7}$$


So $$\Large \frac{1}{x+7}+3$$ simplifies to $$\Large \frac{3x+22}{x+7}$$

Let me know if you can take it from here

anonymous · Answer

I'm still confused on how to get the horizontal asymptote.

jim_thompson5910 · Answer

What are the leading coefficients for $$\Large \frac{3x+22}{x+7}$$

anonymous · Answer

3 and 1?

jim_thompson5910 · Answer

now divide them to get the horizontal asymptote: 3/1 = 3

So the horizontal asymptote is the equation y = 3

anonymous · Answer

oh ok, thanks so much!

jim_thompson5910 · Answer

np