fatimah alzaki 5/3/16 1:1 Chapter 10 Quiz This Question: 1 pt This Test: 18 pts
ID: 2862669 • Letter: F
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fatimah alzaki 5/3/16 1:1 Chapter 10 Quiz This Question: 1 pt This Test: 18 pts 01:53:45 0 of 18 Use- or oo where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. x-4 Locate all zeros of the denominator. Choose the correct answer below. A· There are no zeros of the denominator. OB. f has zeros of the denominator at x -4 and x4. OC. fhas a zero of the denominator at x4 OD, f has a zero of the denominator at x 4. Describe the behavior of ffx) as x approaches the zero(s) of the denominator from the left. Select the correct choice below and fill in any answer boxes within your choice. OA As x approaches the zero(s) of the denominator from the left, fo) approaches (Use a comma to separate answers as needed.) OB. There are no zeros of the denominator Describe the behavior of f(x) as x approaches the zero(s) of the denominator from the night. Select the correct choice below and fill in any answer boxes within your choice. OA Asx approaches the zero(s) of the denominator from the right, fx) approaches OB There are no zeros of the denominator. (Use a comma to separate answers as needed.) Click to sExplanation / Answer
The given function f(x)=1/(x-4)
the function can be used in left and right-hand limits to determine the behavior of the function at x=4
when x=4 the given function has denominator is 0
the left-hand limit
As x approaches 4 from the left the numerator of 1/(x-4) approaches 1 while the denomitator approaches 0 through negative values.This means the fraction 1/(x-4) will approach negative infinity.
lim (x-->4-)of(1/(x-4))=-infinity
the right-hand limit
As x approaches 4 from the right the numerator of 1/(x-4) approaches 1 while the denomitator approaches 0 through positive values.This means the fraction 1/(x-4) will approach positive infinity.
lim (x-->4+)of(1/(x-4))=+ infinity
Therefore x=4 is a vertical asymptote of f(x)=1/(x-4).
behavior of function f(x)=1/(x-4)
As x approaches the zero(s) of the denominator from the left, f(x)=1/(0-4)=-1/4, f(x) approaches -1/4
As x approaches the zero(s) of the denominator from the right, f(x)=1/(0-4)=-1/4, f(x) approaches -1/4
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