This page serves 4 purposes:
- To provide a list of things to do when sketching a polynomial function,
- To provide an example of sketching polynomial 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 polynomial function:|
- · Note the degree of the polynomial
- -- use it to predict the general shape and end behavior.
- -- even functions "start high & end high"
- -- odd functions "start low & end high"
- · Note the coefficient of the term with highest degree
- -- use it to determine if the curve is reflected about the x-axis.
-   x³ "starts low and ends high"
-       (generally increases as x increases)
-   - x³ "starts high and ends low"
-       (generally decreases as x increases)
- · Rewrite it by factoring
- identify the linear, quadratic, or other factors.
- · Plot the real zeros.
- · Note for each root or zero what kind of a root it is
- -- odd powers pass through the x-axis,
- -- even powers touch but do not pass through the x-axis.
- · Plot (0, f(0)), the y-intercept.
- · Solve: first derivative = 0
- -- to find relative maximums/minimums.
- · Determine sign in intervals
- -- using the positiveness or negativeness of each factor.
- -- just "connect the dots."
- · Sketch curve.
1. Sketch and label then check the
2. Sketch and label then check the
Question 19, 20
- 19.   Decompose, factor, the polynomial
- 19a. State the linear factors.
- 19b. State the quadratic factors.
- 19c. State the end behavior of the function when
-         x approaches negative infinity.
- 19d. State the end behavior of the function when
-         x approaches positive infinity.
- 19e. Sketch the graph.
- 20.   Create and state your own polynomial function
-         with the following characteristics.
- It has a double root at -3.
- It has a pair of imaginary roots.
- It has an x-intercept at 6.
- It has a single root at 4.
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