Question

Determine if the following functions are bottom heavy, top heavy, or equal

Answer 1

Answer:

• (a)Bottom-Heavy, y=0

,

• (b)Equal, y=1/3

,

• (c)Top heavy, No horizontal asymptote

Explanation:

• A Rational function is bottom-heavy when ,the degree of the numerator is less than the degree of the denominator,.

,

• A Rational function is top-heavy when ,the degree of the numerator is more than the degree of the denominator,.

,

• It is balanced (or equal) when ,the degree of the numerator is equal to the degree of the denominator,.

Part A

$\frac{x+2}{x^2+4x+11}$

The function is bottom-heavy.

Since the function is bottom-heavy, the horizontal asymptote is:

$y=0$

Part B

$\frac{x^2-5}{3x^2+4}$

The function is equal.

Since the function is equal, divide the leading coefficients to find the horizontal asymptote.

The horizontal asymptote is at y=1/3.

Part C

$\frac{3x^4+x^2-2}{4x^2+3}$

The function is top-heavy.

Since it is top-heavy, it has no horizontal asymptote.