Intermediate Value Theorem on a Closed Real Interval

In the setting of Single-Variable Calculus on an Interval, let $a,b\in\mathbb{R}$ with $a<b$, let $[a,b]$ be the closed interval determined by $a$ and $b$, and let $f:[a,b]\to\mathbb{R}$ be continuous on $[a,b]$. Let $y\in\mathbb{R}$ satisfy either

Then there exists $c\in[a,b]$ such that $f(c)=y$.