How to show a function is continuous [closed]

So I am given the function $f(x)=x^{69420}$ on $\Bbb{R}$ where $\Bbb{R}$ is the real Numbers. How do I show that $f(x)$ is continuous? (I am stuck on this).

My attempt: So I know the definition of a function being continuous at a point $x$ being this: so for any $\varepsilon > 0$ there exists a $\delta$ such that if $y \in (x-\delta, x+\delta)$ then $|f(x)-f(y)|<\varepsilon$. So I need to show this is true for $f(x)=x^{69420}$ for all $x \in \Bbb{R}$. So say I am given a $y$ in $(x-\delta, x+\delta)$, then $|x^{69420} -y^{69420}|$....