I am asked to find an example of a discontinuous function $f:[0,1]\to \mathbb{R}$ where the intermediate value theorem fails. I went over the intermediate value theorem today

Let $f:[a,b]\to \mathbb{R}$ be a continuous function. Suppose that there exists a y such that $f(a)<y<f(b)$ or $f(a)>y>f(b).$ Then there exists a $\text{}\text{}c\in [a,b]$ such that $f(c)=y$.

I understand the theory behind it, however, we did not go over many example of how to use it to solve such problems so I do not really know where to begin

Let $f:[a,b]\to \mathbb{R}$ be a continuous function. Suppose that there exists a y such that $f(a)<y<f(b)$ or $f(a)>y>f(b).$ Then there exists a $\text{}\text{}c\in [a,b]$ such that $f(c)=y$.

I understand the theory behind it, however, we did not go over many example of how to use it to solve such problems so I do not really know where to begin