Understanding Rational Functions

The video tutorial explains how to write an equation for a rational function based on a given graph. It covers identifying intercepts and vertical asymptotes, determining factors for the numerator and denominator, and calculating the constant 'a' using the y-intercept. The tutorial concludes by assembling the complete rational function that matches the graph's characteristics.

What is the y-intercept of the rational function based on the graph?

• 0

• -3

• 3

• -2

Which point is an x-intercept of the function?

• 0

• -3

• 3

• 2

What does a vertical asymptote at x = -2 indicate about the function?

• x + 2 is a factor of the numerator

• x - 2 is a factor of the denominator

• x - 2 is a factor of the numerator

• x + 2 is a factor of the denominator

How does the graph behave as it approaches the vertical asymptote at x = 2?

• No change

• Upward on both sides

• Downward on both sides

• Upward on one side, downward on the other

What does the x-intercept of -3 tell us about the numerator?

• x - 2 is a factor

• x + 3 is a factor

• x + 2 is a factor

• x - 3 is a factor

How many factors of x - 2 are in the denominator if the graph approaches downward on both sides at x = 2?

• Three

• Two

• None

• One

What is the value of 'a' if the y-intercept is -3?

• 3

• -3

• 8

• -8

Which factor is repeated in the denominator due to the behavior at x = 2?

• x - 2

• x + 2

• x + 3

• x - 3

What is the final form of the rational function?

• -8 * (x - 3) / ((x + 2)(x - 2)^2)

• 8 * (x + 3) / ((x - 2)(x + 2)^2)

• 8 * (x - 3) / ((x - 2)(x + 2)^2)

• -8 * (x + 3) / ((x + 2)(x - 2)^2)

What characteristic of the graph helps determine the constant 'a'?

• Vertical asymptote

• Y-intercept

• Horizontal asymptote

• X-intercept