SOLUTION: I am struggling with this problem... any help will be greatly appreciated! Analyze the graph of the rational function r(x)=x^3-8/x-2 a. Factor the numerator and denominator, an

Algebra ->  Rational-functions -> SOLUTION: I am struggling with this problem... any help will be greatly appreciated! Analyze the graph of the rational function r(x)=x^3-8/x-2 a. Factor the numerator and denominator, an      Log On


   

Question 1045196: I am struggling with this problem... any help will be greatly appreciated!
Analyze the graph of the rational function r(x)=x^3-8/x-2
a. Factor the numerator and denominator, and simplify (if possible). What is the domain of R(x)?
b. What are the x- and y-intercepts?
c. What are the vertical, horizontal, and/or oblique asymptotes of R(x)?
d. Divide the x-axis into open intervals using the zeros of the numerator and denominator; then select one point in each interval, and evaluate the function there.
e. Use the calculated points and asymptotes to graph R(x).
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Not what you mean: r(x)=x^3-8/x-2

What you mean but in pure text still: r(x)=(x^3-8)/(x-2)

With rendering tags placed: r%28x%29=%28x%5E3-8%29%2F%28x-2%29

r%28x%29=%28%28x-2%29%28x%5E2%2B2x%2B4%29%29%2F%28x-2%29
almost same as the simpler f%28x%29=x%5E2%2B2x%2B4 but no point ( a hole) for x at 2.

No vertical asymptote
No horizontal asymptote
No oblique asymptote because function just like y=x%5E2%2B2x%2B4 but with one point missing.


Critical x value is at 2.
What about any roots for x%5E2%2B2x%2B4?
zeros for x=%28-2%2B-+sqrt%284-4%2A4%29%29%2F2------Imaginary - no real roots

You can examine unbounded behavior but....

And no x intercepts

Let x=0, and find what is y; the vertical axis intercept.
graph%28400%2C400%2C-8%2C8%2C-2%2C14%2C%28x%5E3-8%29%2F%28x-2%29%29