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) }}}
{{{R(x)= (x^3-5^3) / (x^2-7^2) }}}
{{{R(x)= (x-5)(x^2-5x+25) / (x+7)(x-7) }}}
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( 300, 300, -30, 30, -30, 30,(x^3 - 125) / (x^2 - 49)) }}}