Finding Intercepts in Rational Functions

This video tutorial explains how to find the X and Y intercepts of rational functions. It begins with a general introduction to intercepts, followed by detailed steps to calculate the Y-intercept by setting X to zero and solving for Y. The tutorial then covers finding the X-intercept by setting Y to zero and solving for X. Two example problems are provided to illustrate these concepts, including one that involves factoring a trinomial. The video concludes with a summary of the procedures for finding intercepts.

What is the first step in finding the y-intercept of a rational function?

• Factor the numerator

• Cross multiply the equation

• Set x equal to zero

• Set y equal to zero

When finding the x-intercept, what should y be set to?

• The numerator

• One

• The denominator

• Zero

In the example problem, what is the x-intercept of the function y = 8/(x-3)?

• (0, 8)

• (0, -8/3)

• (3, 0)

• No x-intercept

What happens when you get an unequal expression while finding intercepts?

• There is no y-intercept

• The function is undefined

• The intercepts are equal

• There is no x-intercept

What is the purpose of factoring expressions in rational functions?

• To simplify the process of finding intercepts

• To make the equation longer

• To eliminate the denominator

• To change the function's degree

Which of the following is a factor of the numerator x^2 - 7x + 12?

• x + 4

• x - 4

• x - 3

• x + 3

What is the y-intercept of the function y = (x-3)/(3x+4) after factoring?

• (0, -1/4)

• (0, 1/4)

• (0, 3/4)

• (0, -3/4)

How do you find the x-intercept of a rational function after setting y to zero?

• Solve for y

• Cross multiply and solve for x

• Set x to zero

• Factor the denominator

What is the x-intercept of the function y = (x-3)/(3x+4) after simplification?

• (0, 4)

• (4, 0)

• (0, 3)

• (3, 0)

What is the common factor that can be canceled in the expression (x-4)(x-3)/(x+4)(x-4)?

• x+4

• x-3

• x-4

• x+3