Question

Which statement is true if the degree of the numerator polynomial function is equal to the degree of the denominator polynomial?

Answer 1

Answer:

degree of the denominator`s polynomial function than:

  lim f ( x ) =  ∞

x→∞

Answer: it has no horizontal asymptote.

Step-by-step explanation:

We know that the horizontal asymptote of a function is obtained as follows:

1)

if the degree of the numerator and denominator are equal then we divide the coefficients of the higher degree term.

2)

If the degree of denominator term is greater than the numerator than the horizontal asymptote is the x-axis.

3)

Also if the numerator is of greater degree as compared to the denominator there are no horizontal asymptote.

Hence, in the given question we are given 3) case.

     Hence, there are no horizontal asymptote.

Answer 2

Answer: C. It has only one horizontal asymptote.

Step-by-step explanation:

We know that if the degree of the numerator polynomial function is equal to the degree of the denominator polynomial then , there is only one horizontal asymptote at:

$y=\dfrac{\text{Leading coefficient of numerator }}{\text{Leading coefficient of deniominator}}$

Hence, the statement is true if the degree of the numerator polynomial function is equal to the degree of the denominator polynomial is " It has only one horizontal asymptote."