Final answer:
In the context of continuity of functions and the epsilon-delta definition of a limit, we find that the delta corresponding to epsilon = 1 for the function f(x) = 2x - 5 when c = 3 is delta = 0.5.
Step-by-step explanation:
The student is dealing with a question related to the concept of the continuity of functions and the epsilon-delta definition of a limit in the context of continuous functions. In the given function f(x) = 2x - 5, the value of c = 3 and ε = 1 suggests needing to find the corresponding δ such that for all x in the domain of f(x), if |x - 3| < δ, then |f(x) - f(3)| < 1.
To find δ, we need to work with the function's equation. At x = 3, f(3) = 2(3) - 5 = 1. Therefore, we want |2x - 5 - 1| < 1, which simplifies to |2x - 6| < 1. By solving this inequality, we find that δ = 0.5 because |x - 3| < 0.5 guarantees that the output of the function will be within an epsilon range of 1 unit from the value of the function at c = 3.