SOLUTION: For the function: (x^3+2x^2-4x-8)/2x^2-8 a) Find the domain of the function, and discuss the behavior of f near any excluded x �values. b) Identify all intercepts c) Find all

Question 1027061: For the function: (x^3+2x^2-4x-8)/2x^2-8
a) Find the domain of the function, and discuss the behavior of f near any excluded x �values.
b) Identify all intercepts
c) Find all vertical, horizontal, and slant asymptotes of the graph of the function.
Found 2 solutions by robertb, KMST:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Is the function or ??
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I assume you meant
.
The numerator and denominator of that rational function can be factored.
.
When <---> the denominator is zero,
and the function has no defined value.

a) So, the values are excluded from the domain of the function.
The function can be simplified as
for .
The graph of is a straight line with two holes,
and the behavior of near the excluded values (and everywhere else in its domain)
is just like the behavior of .
In other words, and .

b) The y-intercept of is ,
or the point (0,1) .
is never zero, because where the function exists
it is equal to ,
and only for which is not part of the domain of .
So, there is no x-intercept. The graph of function does not intersect the x-axis; it jumps over it.

c) Since everywhere in its domain ,
the line could be considered the slant asymptote. There is no other asymptote.
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