Understanding Rational Functions

The video tutorial explains how to write an equation for a rational function using its graph. It covers identifying key components such as intercepts and vertical asymptotes, setting up the function in factored form, and determining the constant 'a' using the y-intercept. The tutorial concludes with the finalized rational function.

What is the x-intercept of the rational function as mentioned in the introduction?

• x = 0

• x = 2

• x = -2

• x = 4

Where is the y-intercept located on the graph of the rational function?

• (0, 1)

• (2, 0)

• (0, -1)

• (-2, 0)

What is the significance of a vertical asymptote in a rational function?

• It is the point where the graph crosses the x-axis.

• It shows where the function is undefined.

• It indicates a zero in the numerator.

• It determines the y-intercept.

Which of the following is a vertical asymptote of the function?

• x = 0

• x = 1

• x = 2

• x = -2

What does it mean if the graph touches the x-axis and bounces back at a point?

• The point is a hole in the graph.

• The point has an even multiplicity.

• The point is a vertical asymptote.

• The point is a y-intercept.

How many factors of (x - 2) are needed in the numerator if the graph bounces back at x = 2?

• Two

• Three

• None

• One

What is the value of the constant 'a' in the rational function?

• 1

• 2

• -1

• -2

How is the constant 'a' determined in the rational function?

• By using the x-intercept

• By using the y-intercept

• By using the vertical asymptote

• By using the horizontal asymptote

What is the final form of the rational function derived in the video?

• 2(x - 2)^2 / (x + 2)(x - 4)

• (x - 2)^2 / (x + 2)(x - 4)

• 2(x - 2) / (x + 2)(x - 4)

• (x - 2)^2 / (x - 2)(x + 4)

What is the purpose of the video tutorial?

• To find the derivative of a function

• To solve quadratic equations

• To graph linear functions

• To write an equation for a rational function