Q. 14 - Calculus

Question

Suppose f is a function with f(2) = 5 where for all $ϵ$ > 0, there is some δ > 0 such that if x ∈ (2 − δ, 2) ∪ (2, 2 + δ), then f(x) ∈ (3 − $ϵ$, 3 + $ϵ$). Sketch a possible graph of f.

Step-by-Step Solution

Answer

Step 1. Given information.

We have to sketch a graph of f where f is a function with f(2) = 5 where for all $ϵ$> 0, there is some δ > 0 such that if x ∈ (2 − δ, 2) ∪ (2, 2 + δ), 

Step 2. Sketch a graph.

One possible graph of given conditions is :