SOLUTION: given f(x)=4x^2-1 /x^2-16 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

Question 91475: given f(x)=4x^2-1 /x^2-16

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>4, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.
f. Find the maximum or minimum function value in the interval -4 x 4, and state whether it is a maximum or minimum value for that interval.
g. Describe what happens on the graph when x approaches infinity.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
given f(x)=4x^2-1 /x^2-16
graph(400,300,-10,10,-10,10,(4x^2-1)/(x^2-16))|||
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a. Find the x-intercept(s).
y = 0 when 4x^2-1 = 0; when x=(1/2) or x=(-1/2)
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b. Find the y-intercept(s).
Let x=0; y=-1/-16 = 16
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c. Find the vertical asymptote(s) (write as an equation of a line).
Vertical asymptotes when the denominator is zero:
x=4 or x=-4
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d. Find the horizontal asymptote(s) (write as an equation of a line).
horizontal asyumptote at y = 4/1 = 4
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e. For x>4, is there a value which F(x) cannot exceed, AND/OR a value which F(x) cannot fall below? Explain your answers.
y=4
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f. Find the maximum or minimum function value in the interval -4 x 4, and state whether it is a maximum or minimum value for that interval.
Check the graph of the function.
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g. Describe what happens on the graph when x approaches infinity.
y get closer and closer to 4
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Cheers,
Stan H.
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