Understanding Rational Functions

The video tutorial explains how to write an equation for a rational function based on a given graph. It covers identifying key graph components such as holes, intercepts, and asymptotes. The tutorial then guides viewers through setting up the rational function using these components, determining the constant A using the y-intercept, and finalizing the function. The video concludes with a check of the horizontal asymptote.

What is the first step in writing an equation for a rational function based on a graph?

• Determine the constant 'A'

• Identify the horizontal asymptote

• Use the factored form of the function

• Find the x-intercept

What does a hole in the graph at x = -3 indicate?

• A factor of x + 3 in the numerator only

• A factor of x - 3 in the denominator

• A factor of x + 3 in both numerator and denominator

• A factor of x - 3 in the numerator

Which component of the graph provides information about a factor in the denominator?

• X-intercept

• Y-intercept

• Hole

• Vertical asymptote

How do you determine the value of the constant 'A' in the rational function?

• Using the y-intercept

• Using the x-intercept

• Using the vertical asymptote

• Using the hole

What is the value of 'A' if the function passes through the point (0, -2)?

• 1

• 2

• -2

• -1

What is the degree of the numerator in the final rational function?

• 0

• 1

• 3

• 2

What is the degree of the denominator in the final rational function?

• 1

• 0

• 2

• 3

What is the horizontal asymptote of the rational function?

• x = 1

• x = 0

• y = 0

• y = 1

Why is the horizontal asymptote y = 0 in this rational function?

• The degrees of the numerator and denominator are equal

• The degree of the numerator is less than the denominator

• The function has no horizontal asymptote

• The degree of the numerator is greater than the denominator

What does the horizontal asymptote y = 0 represent in the graph?

• The y-axis

• The x-axis

• A vertical line

• A diagonal line