This page serves 4 purposes:
- To provide a list of things to do when sketching a rational function,
- To provide two examples of sketching rational functions,
- To give you a problems to try and their solution, and
- To assign related questionbook questions on this topic to be
submitted either through email or through the folder on my desk.
You might wish to review how to
notes on a computer.
|To sketch a rational function:|
- · Rewrite it by factoring
- identify the linear, quadratic, and reciprocal factors.
- · Rewrite it by division
- to identify curve shifting.
- · Plot zeros
- -- identified by the real roots of linear or quadratic factors.
- · Mark vertical asymptotes
- -- the roots of denominators of the reciprocal factors.
- · Check for discontinuities or holes
- -- identified by identical factors on the "top" and "bottom" of the fraction.
- · Mark other asymptotes
- -- the
nonremainders part of the quotient from the long division.
- · Determine sign in intervals
- -- using the positiveness or negativeness of each factor.
- · Find end behaviors
- -- the "winner in the battle of the top against the bottom."
- · Set the derivative equal to 0, solve to find x values where the slope is zero
- -- to give the x values of relative maximums, relative minimums, flat spots, discontinuities. (Not shown in these examples.)
- · Sketch curve.
Ex. a. Sketch and label then check the
Ex. b. Sketch and label then check the
Harder Problem, Still the Same Mathematics
- Sketch the graph of .
- Show work then check answer.
Question ratl1, ratl2, and ratl3
- ratl1.   Accurately sketch the graph of .
- ratl2. ratl2a. What is a rational function?
- ratl2b. What's a vertical asymptote?
- ratl2c. What's a horizontal asymptote?
- ratl2d. What's an oblique asymptote?
- ratl2e. Use words and a sketch to answer each question.
- ratl3. Create and state your own rational function with the following
- It has one discontinuity (hole).
- It has a vertical asymptote at x=5.
- It has an x-intercept at -3.
- If it has any other asymptotoes, state their equations.
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function classes page.
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