To find oblique/slant asymptotes, divide the numerator by the denominator. Can you do this?
Here's the problem- Sketch the graph of y=f(x)= x^3+x^2-12x.
Complete the table. x^2-2x-8
Include all intercepts and asymptotes on the graph.
Interval
Test point k
f(k)
sign of f
position of graph
Here's what I put.
x-int= (-4,0(3,0)
y-int= (0,0)
horizontal asymptote= I'm not sure if this is right, but i got x+3
vertical asymptote= x=4 x=-2
It's very hard to write this kind of division out where you can understand what I mean, so take a look at this page on long division of polynomials. It has really good examples and shows all the steps you need.
Once you divide the denom. into the numerator, you'll get a line plus a fraction. The fraction will tend to 0 as x gets larger and larger and your function will approach the line more and more.
Polynomial Long Division: Examples
Instead of long dividing, you cn use the method of comparing coefficients, it's usually quicker.
If you have the function
the it can be written as
Now compare coefficients
Question
Comparing coefficients of x terms