Question

guided practice
the third type of rational function, where the degree of the numerator is equal to the degree of the denominator, can be tricky. lets look at one more example before you try some on your own.
for the rational function $y = \frac{8x^3 + x^2 - 5x + 5}{2x^3 - 3x^2 + 4x + 1}$, the degree of the numerator is 3 and the degree of the denominator is 3.
because the degrees are equal, use $y = \frac{a}{b}$ to find the horizontal asymptote.
type your answers and then click or tap done.
what is the coefficient of the term with the highest degree in the numerator, $a$, and in the denominator, $b$?
$a = \square$
$b = \square$

Explanation:

Step1: Identify numerator's leading term

The numerator is $8z^3 + z^2 - 5z + 5$, leading term is $8z^3$, so $a=8$.

Step2: Identify denominator's leading term

The denominator is $2z^3 - 3z^2 + 4z + 1$, leading term is $2z^3$, so $b=2$.

Answer:

8, 2