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Question
Math
Posted 2 months ago

Function hh is graphed.

Select all correct statements about hh at x=1x=-1.

Choose all answers that apply:
A Both limx1+h(x)\lim _{x \rightarrow-1^{+}} h(x) and limx1h(x)\lim _{x \rightarrow-1^{-}} h(x) exist
B limx1h(x)\lim _{x \rightarrow-1} h(x) exists
c hh is defined at x=1x=-1
D hh is continuous at x=1x=-1
E None of the above
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Answer from Sia
Posted 2 months ago
Solution by Steps
step 2
To determine if limx1h(x) \lim_{x \to -1} h(x) exists, we need both one-sided limits to be equal. Since both one-sided limits approach -5, limx1h(x)=5 \lim_{x \to -1} h(x) = -5 exists
step 3
To determine if h h is defined at x=1 x = -1 , we observe the graph. There is a hole at the point (-1, -5), indicating that h(1) h(-1) is not defined
step 4
To determine if h h is continuous at x=1 x = -1 , the function must be defined at x=1 x = -1 and the limit as x x approaches -1 must equal h(1) h(-1) . Since h(1) h(-1) is not defined, h h is not continuous at x=1 x = -1
A
Key Concept
Existence of Limits
Explanation
For a limit to exist at a point, both one-sided limits must exist and be equal.

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