determine the intervals of continuity for the following function. choose the correct answer below. a…
determine the intervals of continuity for the following function. choose the correct answer below. a. 1,2,(2,3),3,4),(4,6 b. (1,3),3,4),(4,6 c. 1,3),3,4),(4,6 d. 1,2),(2,3),3,4),(4,6
Answer
Explanation:
Step1: Recall continuity definition
A function is continuous at a point if the limit as $x$ approaches that point exists and is equal to the function - value at that point. Discontinuities occur at points where there are jumps, holes, or vertical asymptotes.
Step2: Analyze the graph
From the graph, we can see that there is a hole at $x = 2$ and a jump - like discontinuity at $x=3$.
Step3: Determine the intervals
The function is continuous on the intervals $[1,2)$, $(2,3)$, $[3,4)$, and $(4,6]$.
Answer:
D. $[1,2),(2,3),[3,4),(4,6]$