Transformations
Transformations
Writing Equations
Writing a rational function can be accomplished by adding the asymptote lines to the parent function
. It can also be done by using the rules of transformations.
Example 1 The graph below has a vertical asymptote at x = 2 and a horizontal asymptote at y = -4. What is the equation of the function that models this graph?
![RationalsWriting1-3 RationalsWriting1-3](https://claregladwinresd.glk12.org/pluginfile.php/940/mod_book/chapter/301/Rational_Functions/Images/RationalsWriting1-3.png)
![RationalsWriting1-1 RationalsWriting1-1](https://claregladwinresd.glk12.org/pluginfile.php/940/mod_book/chapter/301/Rational_Functions/Images/RationalsWriting1-1.png)
Example 1 The graph below has a vertical asymptote at x = 2 and a horizontal asymptote at y = -4. What is the equation of the function that models this graph?
![RationalsWriting1-2 RationalsWriting1-2](https://claregladwinresd.glk12.org/pluginfile.php/940/mod_book/chapter/301/Rational_Functions/Images/RationalsWriting1-2.png)
Step 1 . Use the equation of the vertical asymptote to create a part of the rational function.
![RationalsWriting1-3 RationalsWriting1-3](https://claregladwinresd.glk12.org/pluginfile.php/940/mod_book/chapter/301/Rational_Functions/Images/RationalsWriting1-3.png)
Step 2. Use the equation of the horizontal asymptote to create the second part of the rational function.
![RationalsWriting1-4 RationalsWriting1-4](https://claregladwinresd.glk12.org/pluginfile.php/940/mod_book/chapter/301/Rational_Functions/Images/RationalsWriting1-4.png)