review the graph of the function f(x). which statement describes the continuity of the function at x = 1…

review the graph of the function f(x). which statement describes the continuity of the function at x = 1? the function is only left - continuous at x = 1. the function is only right - continuous at x = 1. the function is both left - continuous and right - continuous at x = 1. the function is neither left - continuous nor right - continuous at x = 1.

review the graph of the function f(x). which statement describes the continuity of the function at x = 1? the function is only left - continuous at x = 1. the function is only right - continuous at x = 1. the function is both left - continuous and right - continuous at x = 1. the function is neither left - continuous nor right - continuous at x = 1.

Answer

Explanation:

Step1: Recall continuity definitions

Left - continuity at (x = a) means (\lim_{x\rightarrow a^{-}}f(x)=f(a)), right - continuity at (x = a) means (\lim_{x\rightarrow a^{+}}f(x)=f(a)).

Step2: Analyze the graph at (x = 1)

There is no function value defined at (x = 1) and the graph has no part approaching from the right - hand side of (x = 1). The graph approaches from the left - hand side. Since there is no function value at (x = 1), the function is not left - continuous. And since there is no part of the graph approaching from the right - hand side of (x = 1), it is not right - continuous.

Answer:

The function is neither left - continuous nor right - continuous at (x = 1).