Rational Functions Quiz

Define a rational function.

• A rational function is a function that has a constant value

• A rational function is a function that can be expressed as the quotient or fraction of two polynomial functions, where the denominator function is not equal to zero.

• A rational function is a function that has a linear equation

• A rational function is a function that involves irrational numbers

What is the domain of a rational function?

• All real numbers except for the values that make the denominator zero

• All integers

• Only positive numbers

• Values greater than 10

Explain the concept of vertical asymptotes in rational functions.

• Vertical asymptotes occur when the numerator of the function equals zero.

• Vertical asymptotes are always present in rational functions.

• Vertical asymptotes are horizontal lines in the graph of a rational function.

• Vertical asymptotes in rational functions happen when the denominator of the function equals zero.

How do you find horizontal asymptotes in rational functions?

• Divide the coefficients of the highest degree terms in the numerator and denominator

• Find the average of the x-intercepts

• Look for the x-values where the function is undefined

• Compare the degrees of the numerator and denominator to determine the horizontal asymptote.

Simplify the rational function: (3x^2 + 5x - 2) / (2x^2 - 3x + 1)

• (3x - 1)(x + 2) / (2x + 1)(x - 1)

• (3x + 1)(x - 2) / (2x - 1)(x - 1)

• (3x - 1)(x - 2) / (2x - 1)(x - 1)

• (3x - 1)(x + 2) / (2x - 1)(x - 1)

Find the x-intercepts of the rational function: (x^2 - 4) / (x + 2)

• x = -1, x = 4

• x = -2, x = 2

• x = 0, x = 3

• x = -3, x = 1

What is the end behavior of a rational function?

• The end behavior of a rational function is linear.

• The end behavior of a rational function is always positive.

• The end behavior of a rational function is determined by the leading coefficient of the numerator.

• The end behavior of a rational function depends on the degrees of the numerator and denominator.

Discuss the behavior of a rational function near its vertical asymptotes.

• Near its vertical asymptotes, a rational function behaves by having a horizontal asymptote.

• Near its vertical asymptotes, a rational function behaves by having a vertical tangent.

• Near its vertical asymptotes, a rational function behaves by approaching zero.

• Near its vertical asymptotes, a rational function behaves by approaching positive or negative infinity, potentially having a hole or jump discontinuity, and possibly changing sign.

How do you determine the symmetry of a rational function?

• Count the number of x-intercepts

• Check if the function is continuous

• Check if the function is even, odd, or neither to determine its symmetry.

• Look for vertical asymptotes

Solve the inequality: (x - 3) / (x + 2) > 0

• x < -2 and x < 3

• x < -2 and x > 3

• x < -2 or x > 3

• x > -2 and x > 3