hi guys.. need help in sketching graph and labeling intercepts and asymptotes of the attached function.
it has a power 3 x in the denominator .. how can i solve and simplify it?
thanks!
We may use the rational root theorem: The rational zeros of a polynomial
(if they exist) will be of the form:
So, for example, the possible rational zeros of the numerator are . I find that both x = -1 and x = -2 are zeros of the polynomial. Thus
We can find the remaining zero by long division, synthetic division, or by multiplying the above factorized expression out and solving for p. I get:
You can do a similar factorization of the denominator.
-Dan
Hello, samtrix!
You should be familiar with the Factor Theorem and Remainder Theorem.
(If you're not, I'll let someone else explain them.)
Sketch the graph and label intercepts and asymptotes.
y-intercept: Let and solve for
.
x-intercepts: Let and solve for
. .
Therefore: .
Vertical asymptotes: Value for which the denominator equals zero.
. .
Therefore,
Horizontal asymptote: Find
We have: .
Divide top and bottom by
. . .
Therefore: .