题目
题目

MATH-112-301-001 Unproctored Midcourse 1 Practice Exam 2

单项选择题

Determine which graph satisfies all of these properties: 𝑓 ( 0 ) = 2 ,  lim 𝑥 ⟶ 0 − 𝑓 ( 𝑥 ) = 4 ,  lim 𝑥 ⟶ 0 + 𝑓 ( 𝑥 ) = 2 , lim 𝑥 ⟶ − ∞ 𝑓 ( 𝑥 ) = − ∞ ,  lim 𝑥 ⟶ 4 − 𝑓 ( 𝑥 ) = − ∞ , lim 𝑥 ⟶ 4 + 𝑓 ( 𝑥 ) = ∞ ,  lim 𝑥 ⟶ ∞ 𝑓 ( 𝑥 ) = 3

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思路分析
The provided data for the problem includes a question stem and a set of properties, but there are no answer options given to evaluate against the graph. Without labeled options to compare, we cannot identify which graph satisfies all the listed conditions. What we do have to work with is the list of required properties for f: - f(0) = 2 - limit as x approaches 0 from the left of f(x) = 4 - limit as x approaches 0 from the right of f(x) = 2 - limit as x approaches -infinity of f(x) = -infinity - limit as x approach......Login to view full explanation

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类似问题

Suppose that with a certain phone company, an international long distance phone call from Canada to Brazil costs $0.90 for the first minute (up to and including 60 seconds), plus $0.50 for each additional minute or part of a minute. Note: "Part of a minute" means that if a new minute is started even just by one second, a full minute is charged. For example, a 5 min 1 sec phone call costs the same as a 5 min 50 sec phone call and the same as a 6 min 0 sec phone call.   Suppose 𝐶 ( 𝑡 ) is the function that gives the cost of making a 𝑡 minute long phone call.  On a piece of paper, sketch a graph showing  𝐶 ( 𝑡 ) (with 𝐶 on the 𝑦 -axis and 𝑡 on the 𝑥 -axis). Then use your graph to evaluate each of the following: (Write DNE for undefined.) 𝐶 ( 2.5 ) = [ Select ] DNE 1.9 1.4 2.4 2.9 𝐶 ( 4 ) = [ Select ] 3.4 1.9 2.9 2.4 DNE lim 𝑥 → 3.1 𝐶 ( 𝑡 ) = [ Select ] 1.9 1.4 2.9 2.4 DNE lim 𝑥 → 4 − 𝐶 ( 𝑡 ) = [ Select ] 2.4 1.4 2.9 1.9 DNE lim 𝑥 → 4 + 𝐶 ( 𝑡 ) = [ Select ] DNE 2.9 2.4 3.4 1.9 lim 𝑥 → 4 𝐶 ( 𝑡 ) = [ Select ] 1.9 2.9 DNE 3.4 2.4

Consider this graph of the function  𝑓 ( 𝑥 ) . Which of the following statements are true and which are false?  lim 𝑥 → 3 − 𝑓 ( 𝑥 ) = lim 𝑥 → 3 + 𝑓 ( 𝑥 ) [ Select ] False True lim 𝑥 → 1 𝑓 ( 𝑥 ) = 𝑓 ( 1 )     [ Select ] True False 𝑓 ( 𝑥 )  has a vertical asymptote at 𝑥 = 4 . [ Select ] False True 𝑓 ( 𝑥 )  has a vertical asymptote at 𝑥 = 6  . [ Select ] False True lim 𝑥 → 4 − 𝑓 ( 𝑥 ) = lim 𝑥 → 4 + 𝑓 ( 𝑥 ) [ Select ] False True lim 𝑥 → 4 𝑓 ( 𝑥 ) = ∞ [ Select ] True False lim 𝑥 → 6 𝑓 ( 𝑥 ) = ∞ [ Select ] False True The limit lim 𝑥 → 4 𝑓 ( 𝑥 ) exists, but lim 𝑥 → 6 𝑓 ( 𝑥 )  does not exist. [ Select ] False True

Consider the function 𝑓 ( 𝑥 ) = { 𝑥 2 + 1 𝑖 𝑓 𝑥 < 2 3 𝑖 𝑓 𝑥 = 2 7 − 𝑥 𝑖 𝑓 𝑥 > 2 .  We aim to find out if 𝑓 ( 𝑥 ) has a discontinuity at 𝑥 = 2 , and if so, of what type. In order to do that, first find the following information: 𝑓 ( 2 )  = [ Select ] 5 3 2 7 lim 𝑥 ⟶ 2 − 𝑓 ( 𝑥 )  = [ Select ] 7 3 2 5 lim 𝑥 ⟶ 2 + 𝑓 ( 𝑥 )  = [ Select ] 5 7 2 3 Is 𝑓 ( 𝑥 ) continuous or discontinuous at 𝑥 = 2 ? [ Select ] discontinuous continuous If 𝑓 ( 𝑥 ) is discontinuous at 𝑥 = 2 , what type of discontinuity is it? [ Select ] f is continuous An infinite discontinuity A removable discontinuity A jump discontinuity  

Consider this graph of the function  𝑓 ( 𝑥 ) . Which of the following statements are true and which are false?  lim 𝑥 → 3 − 𝑓 ( 𝑥 ) = lim 𝑥 → 3 + 𝑓 ( 𝑥 ) [ Select ] False True lim 𝑥 → 1 𝑓 ( 𝑥 ) = 𝑓 ( 1 )     [ Select ] False True 𝑓 ( 𝑥 )  has a vertical asymptote at 𝑥 = 4 . [ Select ] True False 𝑓 ( 𝑥 )  has a vertical asymptote at 𝑥 = 6  . [ Select ] False True lim 𝑥 → 4 − 𝑓 ( 𝑥 ) = lim 𝑥 → 4 + 𝑓 ( 𝑥 ) [ Select ] True False lim 𝑥 → 4 𝑓 ( 𝑥 ) = ∞ [ Select ] False True lim 𝑥 → 6 𝑓 ( 𝑥 ) = ∞ False The limit lim 𝑥 → 4 𝑓 ( 𝑥 ) exists, but lim 𝑥 → 6 𝑓 ( 𝑥 )  does not exist. [ Select ] True False

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