Understanding Asymptotes in Rational Functions

What is a rational function composed of?

• A polynomial divided by another polynomial

• A polynomial multiplied by another polynomial

• A polynomial divided by a constant

• Two constants divided by each other

What determines the location of vertical asymptotes in a rational function?

• The real zeros of the denominator

• The leading coefficient of the numerator

• The degree of the numerator

• The zeros of the numerator

When does a rational function have the x-axis as a horizontal asymptote?

• When the numerator is a constant

• When the degrees of the numerator and denominator are equal

• When the degree of the numerator is less than the degree of the denominator

• When the degree of the numerator is greater than the degree of the denominator

In the function f(x) = 2x / (x^2 - 1), what are the vertical asymptotes?

• x = -2

• x = 2

• x = 1 and x = -1

• x = 0

For the function g(x) = (1 - 5x) / (3 + 2x), what is the horizontal asymptote?

• y = -5/2

• y = 1

• y = 0

• y = 3/2

What happens to the horizontal asymptote when the degree of the numerator is greater than the degree of the denominator?

• The horizontal asymptote is y = 0

• There is no horizontal asymptote

• The horizontal asymptote is determined by the leading coefficients

• The horizontal asymptote is y = 1

What is the condition for a rational function to have a slant asymptote?

• The numerator is a constant

• The degree of the numerator is exactly one more than the degree of the denominator

• The degree of the numerator is equal to the degree of the denominator

• The degree of the numerator is one less than the degree of the denominator

How do you find the slant asymptote of a rational function?

• By comparing the leading coefficients

• By setting the numerator equal to zero

• By using polynomial long division

• By finding the zeros of the denominator

In the function h(x) = -2x^3 / (x^2 + 1), why is there no vertical asymptote?

• Because the degrees are equal

• Because the numerator is negative

• Because the numerator is larger

• Because the denominator has no real zeros

What is the slant asymptote for the function with a numerator degree one more than the denominator?

• y = x + 1

• y = 1

• y = 0

• y = -x