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Question 497745: Hi I need help on solving for the Domain, Range, X and Y Intercepts, and Aymptotes of  How would I go about solving for these? Thank you!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Domain, Range, X and Y Intercepts, and Aymptotes of y= 5/x -1
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y= 5/x -1
y=(5-x)/x
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Domain:
Function becomes undefined when x=0
Domain:x≠0
(-∞, 0) U (0, ∞)
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Range:
solve for x in terms of y
xy=5-x
xy+x=5
x(y+1)=5
x=5/(y+1)
Range: y≠-1
(-∞, -1) U (-1, ∞)
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x-intercept:
Set y=0. then solve for x
5-x=0
x=5
x-intercept=5
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y-intercept
set x=0, then solve for y
When x=0, y becomes undefined
y-intercept: none
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Vertical asymptote:
Set denominator =0, then solve for x
vertical asymptote:x=0 or y-axis
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Horizontal Asymptote:
When degree of both numerator and denominator the same, as in this case, divide the coefficient of x in the numerator by the coefficient of x in the denominator. The quotient is the horizontal asymptote. -1/1=-1
Horizontal Asymptote: y=-1
see graph below as a visual check on the answers
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