SOLUTION: I need help on the step by step process on how to analyze the graph of this following function ? R(x)= x^3 - 125 / x^2 - 49 ?

Algebra ->  Rational-functions -> SOLUTION: I need help on the step by step process on how to analyze the graph of this following function ? R(x)= x^3 - 125 / x^2 - 49 ?      Log On


   

Question 635607: I need help on the step by step process on how to analyze the graph of this following function ?
R(x)= x^3 - 125 / x^2 - 49 ?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
I need help on the step by step process on how to analyze the graph of this following function ?
R%28x%29=+%28x%5E3+-+125%29+%2F+%28x%5E2+-+49%29+
R%28x%29=+%28x%5E3-5%5E3%29+%2F+%28x%5E2-7%5E2%29+
R%28x%29=+%28x-5%29%28x%5E2-5x%2B25%29+%2F+%28x%2B7%29%28x-7%29+
Because the degree of the numerator is one degree higher than that of the denominator,
function has a slant asymptote.
..
To find the equation of the slant asymptote, divide denominator by numerator.
By inspection, you can see you will get x+remainder. You can ignore the remainder.
equation of the slant asymptote: y=x
..
x-intercept:
set R(x)=0
x-5=0
x-intercept=5
..
y-intercept:
set x=0
-125/-49≈2.55
y-intercept≈2.55
..
vertical asymptotes:
set denominator=0
x=7
and
x=-7
..
number line:
<..-...-7...+....5....-....7....+.....>
The graph below shows the basic curve but I don't have the means to draw in the asymptotes.
However, it should be good guide how to graph the entire curve with asymptotes and all.
+graph%28+300%2C+300%2C+-30%2C+30%2C+-30%2C+30%2C%28x%5E3+-+125%29+%2F+%28x%5E2+-+49%29%29+