Finding X and Y Intercepts of Rational Functions

The video tutorial covers the process of finding x and y intercepts in rational functions, emphasizing the importance of setting restrictions. It demonstrates how to graph rational functions by identifying intercepts and asymptotes, and explains how to simplify rational functions to identify holes. The tutorial concludes with a section on writing equations for rational functions given specific conditions, using standard form and transformations.

What is the condition for an X-intercept in a rational function?

• X equals 0

• Y equals 0

• X equals 1

• Y equals 1

What should you do first when finding X-intercepts in a rational function?

• Add 1 to both sides

• Divide the denominator

• Multiply the numerator

• Set restrictions

In the example problem, what is the X-intercept for the function after setting restrictions and simplifying?

• X = 7

• X = 3

• X = -7

• X = -3

What is the condition for a Y-intercept in a rational function?

• Y equals 1

• X equals 1

• Y equals 0

• X equals 0

How do you find the Y-intercept for a rational function?

• Set Y to 1

• Set X to 0

• Set Y to 0

• Set X to 1

What is the Y-intercept for the function in the second example problem?

• 0, -1

• 0, 2

• 0, 1

• 0, 3

What is the first step in graphing a rational function?

• Multiply the numerator

• Find the Y-intercept

• Set restrictions

• Find the horizontal asymptote

How do you determine the horizontal asymptote of a rational function?

• Set X to 0

• Compare the degrees of the numerator and denominator

• Multiply the numerator

• Set Y to 0

What is the simplified form of the function in the second example problem after setting restrictions?

• X - 2

• X - 1

• X + 1

• X + 2

What is the purpose of using the standard form when writing equations for rational functions?

• To find the Y-intercept

• To find the X-intercept

• To easily see vertical and horizontal asymptotes

• To multiply the numerator