Understanding Rational Functions

The video tutorial explains how to analyze a rational function by determining its y-intercept, x-intercepts, vertical asymptotes, and horizontal asymptotes. It begins with factoring the numerator and denominator, then proceeds to find the y-intercept by setting x to zero. The x-intercepts are found by setting the numerator to zero, while vertical asymptotes are identified by setting the denominator to zero. Horizontal asymptotes are determined by comparing the degrees of the numerator and denominator. The tutorial concludes with graphing the function to verify the results.

What is the first step in analyzing a rational function?

• Graphing the function

• Factoring the numerator and denominator

• Finding the y-intercept

• Calculating the horizontal asymptote

How do you find the y-intercept of a rational function?

• Set x to zero

• Factor the numerator

• Factor the denominator

• Set y to zero

What is the y-intercept of the function given in the video?

• (0, 3/5)

• (0, -3/5)

• (0, 5/3)

• (0, -5/3)

To find the x-intercepts of a rational function, what must be true?

• Both numerator and denominator must be zero

• The function must be undefined

• The numerator must be zero

• The denominator must be zero

What are the x-intercepts of the function discussed in the video?

• (1/2, 0) and (-5, 0)

• (5, 0) and (-3, 0)

• (0, -1/2) and (0, 5)

• (-1/2, 0) and (5, 0)

How are vertical asymptotes determined in a rational function?

• By setting the numerator to zero

• By setting the denominator to zero

• By finding common factors

• By evaluating the function at infinity

What are the vertical asymptotes of the function in the video?

• x = 5 and x = -5

• x = 0 and x = 1

• x = -1/2 and x = 3

• x = 1/2 and x = -3

What determines the horizontal asymptote of a rational function?

• The sum of the degrees of the numerator and denominator

• The difference in degrees between the numerator and denominator

• The ratio of the leading coefficients if degrees are equal

• The product of the leading coefficients

What is the horizontal asymptote of the function discussed?

• y = 0

• y = 1

• y = -1

• y = 2

If the degree of the numerator is greater than the degree of the denominator, what is true about the horizontal asymptote?

• It is y = 0

• It is y = infinity

• It is y = 1

• There is no horizontal asymptote