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Question 91297: given: F(x) = x/x^2-9
a. Find the x-intercept(s).
b. Find the y-intercept(s).
c. Find the vertical asymptote(s) (write as an equation of a line).
d. Find the horizontal asymptote(s) (write as an equation of a line).
e. For x<-3, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.
f. Is the function increasing or decreasing in the interval -3<- x <- 3?
g. As x approaches 3 from the left, what happens to the function values?
h. As x approaches 3 from the right, what happens to the function values?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! given: F(x) = x/x^2-9
a. Find the x-intercept(s).
Let y=0 and solve for x; y is 0 when the numerator is 0, i.e. when x=0
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b. Find the y-intercept(s).
Let x = 0, they y = 0
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c. Find the vertical asymptote(s) (write as an equation of a line).
Let x^2-9=0 then x=3 of x=-3; these are the vertical asymptotes.
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d. Find the horizontal asymptote(s) (write as an equation of a line).
The coefficients of the highest power term in the numerator and in the
denominator are 0/1; The horizontal asymptote is y=0
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e. For x<-3, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.
You know the horizontal asymptote is y=0. Take a test value like x=-5
to see where the graph is relative to the line y=0.
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f. Is the function increasing or decreasing in the interval -3<- x <- 3?
Take a look at the graph.
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g. As x approaches 3 from the left, what happens to the function values?
Check the graph
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h. As x approaches 3 from the right, what happens to the function values?
Check the graph
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Cheers,
Stan H.
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