Understanding Asymptotes and Graphing Functions

The video tutorial explains how to determine the equations of asymptotes and graph a function. It begins by identifying vertical asymptotes, which occur at the zeroes of the denominator that are not zeroes of the numerator. The tutorial emphasizes the importance of factoring and simplifying the rational function to identify any possible holes. In the example provided, a common factor results in a hole at x = -2, simplifying the function to a line with a hole. The video concludes by graphing the line y = x - 2, noting the absence of vertical and horizontal asymptotes.

What is the first step in determining vertical asymptotes for a rational function?

• Graphing the function

• Finding the zeroes of the numerator

• Finding the zeroes of the denominator

• Simplifying the function

Why is it important to factor and simplify a rational function before determining vertical asymptotes?

• To calculate the slope

• To determine the y-intercept

• To identify any common factors that may indicate a hole

• To find the x-intercepts

What happens when a zero of the denominator is also a zero of the numerator?

• The function becomes undefined

• A hole is formed

• A horizontal asymptote is formed

• A vertical asymptote is formed

After simplifying the function, what type of graph is obtained?

• A parabola

• A circle

• A line

• A hyperbola

What is the equation of the line obtained after simplification?

• y = x + 2

• y = x - 2

• y = 2x - 2

• y = -x + 2

What is the y-intercept of the line y = x - 2?

• -2

• 0

• 2

• 1

What is the slope of the line y = x - 2?

• 0

• 1

• -1

• 2

Where is the hole located on the graph of the function?

• At x = 2

• At y = -2

• At x = -2

• At y = 2