Rational Functions Characteristics and Analysis

The video tutorial explains how to find an equation for a rational function with given vertical asymptotes, x-intercepts, and a y-intercept. It covers the setup of the function in factored form, using the asymptotes to determine the denominator factors, and the x-intercepts for the numerator factors. The tutorial also demonstrates how to use the y-intercept to solve for the constant A, resulting in a complete rational function that meets all specified characteristics.

What are the given vertical asymptotes for the rational function?

• x = -2 and x = 4

• x = -4 and x = 8

• x = -1 and x = 7

• x = -3 and x = 5

Which of the following is a given x-intercept for the rational function?

• x = -3

• x = 5

• x = 0

• x = -2

If x = -4 is a vertical asymptote, what must be a factor of the denominator?

• x - 4

• x - 8

• x + 8

• x + 4

What does the presence of vertical asymptotes indicate about the rational function?

• The function is undefined at those points

• The function is zero at those points

• The function has a maximum at those points

• The function has a minimum at those points

If x = 4 is an x-intercept, what must be a factor of the numerator?

• x + 4

• x - 4

• x - 2

• x + 2

What does the y-intercept of the rational function help determine?

• The factors in the numerator

• The factors in the denominator

• The degree of the function

• The value of the constant A

What is the y-intercept of the rational function?

• 1

• 0

• 2

• 3

What is the value of the constant A in the rational function?

• 4

• 6

• 8

• 10

Which of the following is NOT a characteristic of the rational function described?

• Vertical asymptotes at x = -4 and x = 8

• X-intercepts at x = -2 and x = 4

• Y-intercept at y = 3

• Constant A equals 8

What is the equation of the rational function in factored form?

• F(x) = 8(x+4)(x-8)/(x-2)(x+2)

• F(x) = 8(x-2)(x+4)/(x-4)(x+8)

• F(x) = 8(x-4)(x+8)/(x+2)(x-4)

• F(x) = 8(x+2)(x-4)/(x+4)(x-8)