SOLUTION: let f(x) = x^3-2x^2/x^2-1. find the following a. vertical asymptote(s) b. slant asymptote c. x intercepts d. y intercepts

Algebra ->  Functions -> SOLUTION: let f(x) = x^3-2x^2/x^2-1. find the following a. vertical asymptote(s) b. slant asymptote c. x intercepts d. y intercepts      Log On


   

Question 1158970: let f(x) = x^3-2x^2/x^2-1. find the following
a. vertical asymptote(s)
b. slant asymptote
c. x intercepts
d. y intercepts
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
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(x^3-2x^2)/(x^2-1)
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Grouping symbols are put to show what you most likely really have.

Factored, the expression is %28x%5E2%28x-2%29%29%2F%28%28x-1%29%28x%2B1%29%29.

x intercepts at 0 and 2.
vertical asymptotes at -1 and +1.

Only gave answers to two of the questions.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Vertical asymptotes occur where the denominator of a rational function is zero. Take the denominator function and set it equal to zero. Solve. Then for each root , there is a vertical asymptote with equation

Slant asymptotes occur where the degree of the numerator function is larger than the degree of the denominator function. The equation of the slant asymptote is the quotient resulting from polynomial long division of the denominator into the numerator, excluding any remainder.

-intercepts occur wherever the numerator function has a zero. For all zeros of the numerator function there is an -intercept at the point

The intercept is at the point where is the value of the function when


John

My calculator said it, I believe it, that settles it