find the x - value(s) where the graph is not continuous.\nthe x - value(s) where the function is not…

find the x - value(s) where the graph is not continuous.\nthe x - value(s) where the function is not continuous is/are ( x=square ).\n(use a comma to separate answers as needed.)

find the x - value(s) where the graph is not continuous.\nthe x - value(s) where the function is not continuous is/are ( x=square ).\n(use a comma to separate answers as needed.)

Answer

Explanation:

Step1: Recall the definition of continuity

A function (y = f(x)) is continuous at (x = a) if (\lim_{x\rightarrow a^{-}}f(x)=\lim_{x\rightarrow a^{+}}f(x)=f(a)). Discontinuities occur when this condition is violated.

Step2: Analyze the graph

Looking at the graph, we check for points where there are breaks, jumps, or holes.

  • At (x = 2), there is a hole (the left - hand limit and the right - hand limit exist but (f(2)) is not equal to the limit of the function as (x) approaches (2)).
  • At (x = 6), there is a hole (the left - hand limit and the right - hand limit exist but (f(6)) is not equal to the limit of the function as (x) approaches (6)).

Answer:

(2,6)