Question

How to find the x and y intercepts of a rational function?

A) Rational function factorization method
B) Rational function long division method
C) Rational function synthetic division method
D) Rational function quadratic formula method

Answer 1

To find the x and y intercepts of a rational function, you can use the rational function factorization method. This method involves steps such as finding the x-intercepts, vertical asymptotes, horizontal asymptotes, and sketching the graph of the function.

Step-by-step explanation:

To find the x and y intercepts of a rational function, you can use the rational function factorization method. Here are the steps:

1. Set the numerator equal to zero to find the x-intercepts.
2. Solve the equation for x to find the x-intercepts.
3. Set the denominator equal to zero to find the vertical asymptotes (if any).
4. Solve the equation for x to find the vertical asymptotes.
5. Set the numerator equal to zero and solve for x to find the horizontal asymptotes (if any).
6. Set the denominator equal to zero and solve for x to find the vertical asymptotes.
7. Plug in a few x-values on either side of the x-intercepts, vertical asymptotes, and horizontal asymptotes to determine the behavior of the graph.
8. Plot the x-intercepts, vertical asymptotes, horizontal asymptotes, and points determined in the previous step to sketch the graph of the rational function.

Answer 2

To find the x and y intercepts of a rational function, you can use the rational function factorization method. This method involves steps such as finding the x-intercepts, vertical asymptotes, horizontal asymptotes, and sketching the graph of the function.

Step-by-step explanation:

To find the x and y intercepts of a rational function, you can use the rational function factorization method. Here are the steps:

1. Set the numerator equal to zero to find the x-intercepts.
2. Solve the equation for x to find the x-intercepts.
3. Set the denominator equal to zero to find the vertical asymptotes (if any).
4. Solve the equation for x to find the vertical asymptotes.
5. Set the numerator equal to zero and solve for x to find the horizontal asymptotes (if any).
6. Set the denominator equal to zero and solve for x to find the vertical asymptotes.
7. Plug in a few x-values on either side of the x-intercepts, vertical asymptotes, and horizontal asymptotes to determine the behavior of the graph.
8. Plot the x-intercepts, vertical asymptotes, horizontal asymptotes, and points determined in the previous step to sketch the graph of the rational function.