Prove that $a^x$ is continuous

I'm having trouble with proving the following:

Let $a > 0$ be a positive real number. Show that the function $f : \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x) := a^x$ is continuous.

I'm a first year mathematics student, so I am trying to prove this in a way that is understandable to me, a delta epsilon proof. Could you help me with this?

Thanks in advance!