Question 443633: I have been trying to solve the below problem for some time now,
Determine the vertical and horizontal asymptotes of f(x) = (x)/(x+2)
and graph your solution.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I have been trying to solve the below problem for some time now,
Determine the vertical and horizontal asymptotes of f(x) = (x)/(x+2)
and graph your solution.
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To find vertical asymptotes: Set denominator=0, then solve for x.
x+2=0
x=-2 is a vertical asymptote
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If the degree of the denominator is less than the degree of the denominator, the horizontal asymptote is the x-axis or y=0. (Not in this given case.)
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If the degree of the denominator is equal to the degree of the denominator, divide the coefficient of the numerator by the coefficient of the denominator. The resulting quotient is the horizontal asymptote. In this given case it is 1/1=1, that is, the horizontal asymptote is y=1
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Before drawing the graph of given rational function, you should also find the x and y-intercepts.
To find the x-intercept, set f(x)=0, which makes the numerator=0, so in this case, the x-intercept=0. To find the y-intercept, set x=0 and solve for y. As you can see, this would also make the y-intercept=0.
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You now have all the information you need to plot the curve except to know whether the curve is above or below the x-axis when x>0. You can determine this by noticing that the function will be positive for x>0. See the graph below. Green line is horizontal asymptote. Vertical asymptote does not show.
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y=x/(x+2)
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