Understanding Asymptotes and Graphing Functions

The video tutorial explains how to determine and graph asymptotes of a given function. It starts with identifying vertical asymptotes by checking for common factors in the numerator and denominator. The tutorial then discusses horizontal asymptotes using limits and introduces slant asymptotes when the numerator's degree is higher. A long division method is used to find the slant asymptote equation. Finally, the function is graphed by plotting points and considering the asymptotes.

What is the first step in determining vertical asymptotes?

• Evaluate the limit as x approaches infinity.

• Perform polynomial division.

• Find the zeros of the numerator.

• Check if the numerator and denominator have common factors.

Where does the vertical asymptote occur for the given function?

• x = 1

• x = 2

• x = 0

• x = -1

What condition indicates that a function does not have a horizontal asymptote?

• The degree of the numerator is less 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 greater than the degree of the denominator.

• The numerator and denominator have common factors.

What type of asymptote is present when the degree of the numerator is one higher than the denominator?

• No asymptote

• Slant or oblique asymptote

• Horizontal asymptote

• Vertical asymptote

What is the equation of the slant asymptote for the given function?

• y = x

• y = x - 1

• y = x + 1

• y = 2x + 1

What is the y-intercept of the slant asymptote?

• 0

• +2

• -1

• +1

What is the slope of the slant asymptote?

• 2

• 1

• 0

• -1

What is the y-value when x = 0 for the given function?

• 0

• 3

• -3

• 1

What is the y-value when x = 2 for the given function?

• 5

• 6

• 7

• 8

What is the y-value when x = -1 for the given function?

• -1

• 0

• 2

• -2