Question 568293: 4/x^2+3x-10 how do you find the holes and graph this equation? What is the method to solving this step by step?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 4/x^2+3x-10 how do you find the holes and graph this equation? What is the method to solving this step by step?
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The first step is to write the equation in factored form:
y=4/(x^2+3x-10)=4/(x+5)(x-2)
y-intercept: none (because numerator is a constant)
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x-intercept: set x=0, then solve for y
y=4/-10=-2/5=-.4
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Horizontal asymptote: lf the degree of the numerator is less than the degree of the denominator, horizontal asymptote is the x-axis or y=0.
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Vertical asymptotes: Set denominator=0, then solve for x:
(x+5)(x-2)=0
x=-5
and
x=2
so you have vertical asymptotes at x=-5 and x=2
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and lastly, draw a number line with the zeros on it:
<...+.....-5.....-.......2.....+......>
This shows from (-∞,-5) the function is>0
Between (-5,2) the function<0
From(2,∞) the function is again>0
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You now have all the information you need to graph the function.
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