SOLUTION: (6 pts) Given f(x)=|x-7| and g(x)=|x+5|, which of the following is the domain of the quotient function ? Briefly explain. Answer_______ A. (-

Algebra ->  Graphs -> SOLUTION: (6 pts) Given f(x)=|x-7| and g(x)=|x+5|, which of the following is the domain of the quotient function ? Briefly explain. Answer_______ A. (-      Log On


   

Question 1134050: (6 pts) Given f(x)=|x-7| and g(x)=|x+5|, which of the following is the domain of the quotient function ? Briefly explain.
Answer_______
A. (-5,∞)
B. (-∞,-5) ∪ (-5,7) ∪ (7,∞)
C. (-7,-5) ∪ (-5,∞)
D. (-∞,-5)∪(-5,∞)

Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given f%28x%29=abs%28x-7%29 and g%28x%29=abs%28x%2B5%29,
the quotient function:
f%28x%29%2Fg%28x%29=abs%28x-7%29%2Fabs%28x%2B5%29
domain: since denominator can not be equal to zero, exclude values that will make denominator equal to zero
x%2B5%3C%3E0
x%3C%3E-5
domain is: {x element R : x<>-5}
(-infinity,-5%29+U+%28%7B%7B%7B-5,infinity)

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so, answer is:
D. (-infinity,-5%29+U+%28%7B%7B%7B-5,infinity)


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the function is abs(x-7) / abs(x+5)

abs(x+5) is in the denominator.

the denominator will be 0 when x = -5

therefore there is a vertical asymptote at x = -5

both the numerator and the denominator can only be 0 or positive since both numerator and denominator expression are within the absolute value signs.

this means that the overall function will always be greater than or equal to zero because a positive divided by a positive is always positive.

consequently, all values of the function f(x) / g(x) will be positive except at x = -5 when the function has a vertical asymptote.

the graph of the function is shown below.

first is a near end view.
next is a far end view.

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