Math Problem Statement
Function [h] is graphed. Function h is graphed. The x-axis goes from negative 10 to 10. The graph consists of 2 curves. The first curve starts in quadrant 2, moves downward and ends at an open circle at (negative 1, 3). The second curve starts at an open circle at (negative 1, negative 5), moves upward to about (1, negative 4.8), moves downward to about (7, negative 5.8), moves upward, and ends at about (10, negative 4.2). [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [\small{\llap{-}2}] [\small{\llap{-}3}] [\small{\llap{-}4}] [\small{\llap{-}5}] [\small{\llap{-}6}] [\small{\llap{-}7}] [\small{\llap{-}8}] [\small{\llap{-}9}] [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{5}] [\small{6}] [\small{7}] [\small{8}] [\small{9}] [\small{\llap{-}2}] [\small{\llap{-}3}] [\small{\llap{-}4}] [\small{\llap{-}5}] [\small{\llap{-}6}] [\small{\llap{-}7}] [\small{\llap{-}8}] [\small{\llap{-}9}] [y] [x] [y=h(x)] Select all correct statements about [h] at [x=-1]. Choose all answers that apply: Choose all answers that apply: (Choice A) Both
[\displaystyle\lim_{x\to -1^{+}}h(x)] and
[\displaystyle\lim_{x\to -1^{-}}h(x)] exist A Both
[\displaystyle\lim_{x\to -1^{+}}h(x)] and
[\displaystyle\lim_{x\to -1^{-}}h(x)] exist (Choice B)
[\displaystyle\lim_{x\to -1}h(x)] exists B
[\displaystyle\lim_{x\to -1}h(x)] exists
(Choice C)
[h] is defined at
[x=-1]
C
[h] is defined at
[x=-1]
(Choice D)
[h] is continuous at
[x=-1]
D
[h] is continuous at
[x=-1]
(Choice E) None of the above
E
None of the above
Solution
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Math Problem Analysis
Mathematical Concepts
Limits
Continuity
Graph Interpretation
Formulas
One-sided limits: lim(x → a⁻) f(x), lim(x → a⁺) f(x)
Two-sided limits: lim(x → a) f(x)
Theorems
Limit Existence Theorem
Continuity Conditions
Suitable Grade Level
Grades 10-12