Intermediate value theorem

Let $𝐼 = [𝑎, 𝑏]$ and $𝑓 \in 𝖳 𝗈 𝗉 (𝐼, ℝ)$ be a continuous function. Then $𝑓 (𝐼)$ is a closed interval containing $[m i n {𝑓 (𝑎), 𝑓 (𝑏)}, m a x {𝑓 (𝑎), 𝑓 (𝑏)}] .$ anal