http://www.ck12.org Chapter 2. Polynomials and Rational Functions
- There are an infinite number of possible solutions. The key is to create a function that may work and then use
the sign testing procedure to check. Here is one possibility.
f(x) = −x7
10 (x− 1 )^2 (x− 2 )^2 (x− 4 )^2- The vertical asymptotes occur atx= 0 ,−^12. Therefore thexvalues to sign test are -.001, 0.001, 3.999, 4.0001.
f(− 0. 001 ) = +
f( 0. 001 ) =−
f( 3. 999 ) =−
f( 4. 0001 ) = +Practice
Consider the function below for questions 1-4.
f(x) =(x−^2 )(^4) (x+ 1 )(x+ 3 )
x^3 (x+ 3 )(x− 4 )
- Identify the vertical asymptotes.
- Will this function have an oblique asymptote? A horizontal asymptote? If so, where?
- What values will you need to use the sign test with in order to help you make a sketch of the graph?
- Use the sign test and sketch the graph near the vertical asymptotes.
Consider the function below for questions 5-8.
g(x) =^3 (x−^2 )(^2) (x− 1 ) (^2) (x+ 1 )(x+ 3 )
15 x^2 (x+ 5 )(x+ 1 )(x− 3 )^2