Finding Asymptotes and Zeros in Rational Functions

The video tutorial covers the final problem of the unit, focusing on rational functions. It begins with a review of previous examples and introduces the concept of degrees in numerators and denominators, leading to the identification of horizontal asymptotes. The tutorial then explains the process of factoring to find holes in the graph and concludes with determining vertical asymptotes and zeros. The instructor emphasizes understanding these concepts through practical examples and encourages students to apply the knowledge independently.

What is the primary reason the teacher is excited about the final problem?

• It's the last problem of the unit.

• It signifies the end of the course.

• It's a challenging problem.

• It's a fun problem to solve.

How do you determine the horizontal asymptote when the degrees of the numerator and denominator are equal?

• Subtract the leading coefficients.

• Divide the leading coefficients.

• Multiply the leading coefficients.

• Add the leading coefficients.

What is the value of the horizontal asymptote?

• y = 2

• y = 0

• y = 1

• y = -1

What is the significance of the leading coefficients in determining the horizontal asymptote?

• They are added together.

• They are multiplied together.

• They are divided.

• They have no significance.

What method is used to factor both the numerator and the denominator?

• Cross-multiplication

• Slide and divide

• Quadratic formula

• Graphing

What does the 'slide and divide' method help with?

• Identifying the zeros of the function

• Factoring polynomials

• Finding the leading coefficients

• Determining the horizontal asymptote

How is a hole in the graph identified?

• By finding a common factor that cancels out

• By adding the exponents

• By setting the denominator to zero

• By dividing the coefficients

What is the x-coordinate of the hole identified in the problem?

• x = 1

• x = 2

• x = -1

• x = -2

Where does the graph have a vertical asymptote?

• x = 1

• x = 2

• x = -2

• x = -1

At what x-value does the graph hit the x-axis?

• x = 3

• x = -3

• x = 1

• x = -1