Understanding Rational Functions from Graphs

The video tutorial explains how to determine the equation of a rational function from its graph. It covers identifying x and y intercepts, understanding vertical asymptotes, and using these properties to set up the rational function in factored form. The tutorial also demonstrates how to calculate the constant 'a' using the y-intercept, ensuring the function matches the graph's behavior.

What is the significance of the x-intercept in determining the factors of a rational function?

• It affects the vertical asymptotes.

• It is irrelevant to the function's equation.

• It provides information about the factors of the numerator.

• It determines the constant 'a'.

How does the behavior of the graph at an x-intercept affect the rational function?

• It determines the number of factors in the numerator.

• It changes the constant 'a'.

• It affects the horizontal asymptote.

• It has no effect on the function.

What does a vertical asymptote at x = -1 indicate about the denominator?

• It has a factor of x + 1.

• It has a factor of x - 1.

• It has no factors related to x.

• It has a factor of x + 2.

Why are there two factors of x + 1 in the denominator?

• Because the graph crosses the x-axis at x = 1.

• Because the graph approaches the vertical asymptote downward on both sides.

• Because the graph has a horizontal asymptote at y = 0.

• Because the graph has a y-intercept at -2.

What is the role of the y-intercept in determining the rational function?

• It affects the degree of the denominator.

• It determines the factors of the numerator.

• It is used to calculate the constant 'a'.

• It helps find the vertical asymptotes.

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

• By using the x-intercept.

• By using the y-intercept.

• By using the vertical asymptotes.

• By using the horizontal asymptote.

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

• One

• Two

• Three

• Four

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

• Three

• Four

• Two

• One

What is the horizontal asymptote of the rational function?

• y = 1

• y = 2

• y = -1

• y = 0

Why does the graph approach the x-axis to the left and right?

• Because the graph has no vertical asymptotes.

• Because the degree of the numerator is equal to the degree of the denominator.

• Because the degree of the numerator is less than the degree of the denominator.

• Because the degree of the numerator is greater than the degree of the denominator.