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