Question

How do you find vertical, horizontal and oblique asymptotes for `g(x)=5^x`?

Answer 1

There will be a horizontal asymptote at `y = 0`.

Explanation:

The domain of any exponential function is `{x| x in RR}`, so no vertical asymptotes.

As for horizontal asymptotes, the following limit will be determinative:

`lim_(x-> -oo) 5^x`

Calling the limit `L`, we have:

`L = lim_(x->-oo) 5^x`

If we think about it, we realize that the closer the number `x = a` gets to `-oo`, the closer `L` will get to `0`. This is because `a^-n = 1/a^n`, and `1/oo = 0`.

So something like `5^-1000` would be very close to `0`. Therefore, we can say that `g(x)` has a horizontal asymptote at `y = 0`.

There will be no oblique asymptote for `g(x)`.

Hopefully this helps!