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Determine which graph satisfies all of the following conditions: lim ๐‘ฅ โŸถ โˆ’ 4 โˆ’ ๐‘“ ( ๐‘ฅ ) = โˆ’ 1 ย  lim ๐‘ฅ โŸถ โˆ’ 4 + ๐‘“ ( ๐‘ฅ ) = 1 ย  lim ๐‘ฅ โŸถ 3 ๐‘“ ( ๐‘ฅ ) = โˆ’ โˆž ย  lim ๐‘ฅ โŸถ โˆ’ โˆž ๐‘“ ( ๐‘ฅ ) = 2 ย  lim ๐‘ฅ โŸถ + โˆž ๐‘“ ( ๐‘ฅ ) = 2 ย  ๐‘“ ( โˆ’ 4 ) = 5 ย 

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To determine which graph satisfies all given conditions, let's parse each condition and compare it to the features a graph would need to display. - Condition: lim_{x -> -4^-} f(x) = -1 and lim_{x -> -4^+} f(x) = 1, with f(-4) = 5. This implies a jump discontinuity at x = -4: the left-hand limit should approach -1, the right-hand limit should approach 1, and there should be a solid point at x = -4 with y = 5 indicating the function value there. A correct graph must show a vertical gap or jump as x passes -4, with the two one-sided limits approaching the specified values, and ......Login to view full explanation

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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. ย  Suppose ๐ถ ( ๐‘ก ) is the function that gives the cost of making a ๐‘ก minute long phone call.ย  On a piece of paper, sketch a graph showingย  ๐ถ ( ๐‘ก ) (with ๐ถ on the ๐‘ฆ -axis and ๐‘ก on the ๐‘ฅ -axis). Then use your graph to evaluate each of the following: (Write DNE for undefined.) ๐ถ ( 2.5 ) = [ Select ] DNE 1.9 1.4 2.4 2.9 ๐ถ ( 4 ) = [ Select ] 3.4 1.9 2.9 2.4 DNE lim ๐‘ฅ โ†’ 3.1 ๐ถ ( ๐‘ก ) = [ Select ] 1.9 1.4 2.9 2.4 DNE lim ๐‘ฅ โ†’ 4 โˆ’ ๐ถ ( ๐‘ก ) = [ Select ] 2.4 1.4 2.9 1.9 DNE lim ๐‘ฅ โ†’ 4 + ๐ถ ( ๐‘ก ) = [ Select ] DNE 2.9 2.4 3.4 1.9 lim ๐‘ฅ โ†’ 4 ๐ถ ( ๐‘ก ) = [ Select ] 1.9 2.9 DNE 3.4 2.4

Consider this graph of the functionย  ๐‘“ ( ๐‘ฅ ) . Which of the following statements are true and which are false?ย  lim ๐‘ฅ โ†’ 3 โˆ’ ๐‘“ ( ๐‘ฅ ) = lim ๐‘ฅ โ†’ 3 + ๐‘“ ( ๐‘ฅ ) [ Select ] False True lim ๐‘ฅ โ†’ 1 ๐‘“ ( ๐‘ฅ ) = ๐‘“ ( 1 ) ย  ย  [ Select ] True False ๐‘“ ( ๐‘ฅ ) ย has a vertical asymptote at ๐‘ฅ = 4 . [ Select ] False True ๐‘“ ( ๐‘ฅ ) ย has a vertical asymptote at ๐‘ฅ = 6 ย . [ Select ] False True lim ๐‘ฅ โ†’ 4 โˆ’ ๐‘“ ( ๐‘ฅ ) = lim ๐‘ฅ โ†’ 4 + ๐‘“ ( ๐‘ฅ ) [ Select ] False True lim ๐‘ฅ โ†’ 4 ๐‘“ ( ๐‘ฅ ) = โˆž [ Select ] True False lim ๐‘ฅ โ†’ 6 ๐‘“ ( ๐‘ฅ ) = โˆž [ Select ] False True The limit lim ๐‘ฅ โ†’ 4 ๐‘“ ( ๐‘ฅ ) exists, but lim ๐‘ฅ โ†’ 6 ๐‘“ ( ๐‘ฅ ) ย does not exist. [ Select ] False True

Consider the function ๐‘“ ( ๐‘ฅ ) = { ๐‘ฅ 2 + 1 ๐‘– ๐‘“ ๐‘ฅ < 2 3 ๐‘– ๐‘“ ๐‘ฅ = 2 7 โˆ’ ๐‘ฅ ๐‘– ๐‘“ ๐‘ฅ > 2 .ย  We aim to find out if ๐‘“ ( ๐‘ฅ ) has a discontinuity at ๐‘ฅ = 2 , and if so, of what type. In order to do that, first find the following information: ๐‘“ ( 2 ) ย = [ Select ] 5 3 2 7 lim ๐‘ฅ โŸถ 2 โˆ’ ๐‘“ ( ๐‘ฅ ) ย = [ Select ] 7 3 2 5 lim ๐‘ฅ โŸถ 2 + ๐‘“ ( ๐‘ฅ ) ย = [ Select ] 5 7 2 3 Is ๐‘“ ( ๐‘ฅ ) continuous or discontinuous at ๐‘ฅ = 2 ? [ Select ] discontinuous continuous If ๐‘“ ( ๐‘ฅ ) is discontinuous at ๐‘ฅ = 2 , what type of discontinuity is it? [ Select ] f is continuous An infinite discontinuity A removable discontinuity A jump discontinuity ย 

Consider this graph of the functionย  ๐‘“ ( ๐‘ฅ ) . Which of the following statements are true and which are false?ย  lim ๐‘ฅ โ†’ 3 โˆ’ ๐‘“ ( ๐‘ฅ ) = lim ๐‘ฅ โ†’ 3 + ๐‘“ ( ๐‘ฅ ) [ Select ] False True lim ๐‘ฅ โ†’ 1 ๐‘“ ( ๐‘ฅ ) = ๐‘“ ( 1 ) ย  ย  [ Select ] False True ๐‘“ ( ๐‘ฅ ) ย has a vertical asymptote at ๐‘ฅ = 4 . [ Select ] True False ๐‘“ ( ๐‘ฅ ) ย has a vertical asymptote at ๐‘ฅ = 6 ย . [ Select ] False True lim ๐‘ฅ โ†’ 4 โˆ’ ๐‘“ ( ๐‘ฅ ) = lim ๐‘ฅ โ†’ 4 + ๐‘“ ( ๐‘ฅ ) [ Select ] True False lim ๐‘ฅ โ†’ 4 ๐‘“ ( ๐‘ฅ ) = โˆž [ Select ] False True lim ๐‘ฅ โ†’ 6 ๐‘“ ( ๐‘ฅ ) = โˆž False The limit lim ๐‘ฅ โ†’ 4 ๐‘“ ( ๐‘ฅ ) exists, but lim ๐‘ฅ โ†’ 6 ๐‘“ ( ๐‘ฅ ) ย does not exist. [ Select ] True False

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