Question 535628: How would you graph this: x-2/(x-3)(x+2)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How would you graph this: x-2/(x-3)(x+2)
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y-intercept
set x=0
y=-2/-3*-2=-2/-6=1/3
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x-intercept
set y=0
x-2=0
x=2
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Horizontal Asymptote:
Degree of numerator is one less than degree of denominator; therefore, the horizontal asymptote is the x-axis or y=0
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Vertical Asymptotes:
set denominator=0, then solve for x
(x-3)(x+2)=0
x=3 and -2
Vertical asymptotes at x=3 and x=-2
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And the number line as another aid for graphing given function:
<.....-....-2......+.....2....-.....3....+.....>
Drawing the number line:
By inspection it can be seen that when x>3, the function>0
Moving to the left, each time we go thru a zero as shown on the graph, the sign of the following interval switches signs if the zero is of odd multiplicity like 1, 3, 5, etc. Given zeros are all of multiplicity 1.
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You now have the y and x intercepts, the horizontal asymptote, vertical asymptotes and number line with which you should easily be able to graph given function.
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