Learning Resources
Outcomes
By the end of this lesson you will be able to answer questions like the ones in the pre-test below.
Approach #1
Answer the questions on the pre-test below in your Math 3103 binder. Then refer to the pages of the lesson that contain instruction on the questions you were unable to do, for which you got an incorrect answer, or for which you would like some further explanation.
Approach #2
Proceed directly to the first page of the lesson without attempting the pre-test. To do this simply click on the Lesson button above. You can then return to this pre-test later and use it as a worksheet.
Pre-test
Identify the real zeros (where they exist) and use your knowledge of its "basic shape" to help sketch the graph of each of the following functions. Do not use graphing technology other than as a check of your work.
1. f(x) = (x - 1)(x - 3)(x + 2) 2. f(x) = - (x - 1)(x - 3)(x + 2)
3. f(x) = (x + 4)(x - 1)2 4. f(x) = (x - 2)3
5. f(x) = -(x + 1)(x + 2)2 6. f(x) = x3 + 3x2 - x - 3
7. f(x) = (x + 2)(x + 3)(x - 4)(x - 1) 8. f(x) = - (x + 2)(x + 3)(x - 4)(x - 1)
9. f(x) = (x + 2)2(x - 4)(x - 1) 10. f(x) = (x + 2)3(x - 4)
11. f(x) = (x + 2)4 12. f(x) = x4 - 13x2 + 36
Students will be expected to:
- Recognize and draw basic graphs of polynomial functions to degree 4.
- Use graphs to obtain precise polynomial functions.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- Functional notation.
- The concept of the zero of a function.
- How to find the x-intercept of the graph of a function.
- The relation between the zeros of a function and the x-intercepts of its graph.
- How to sketch the graphs of constant, linear, and quadratic functions using their zeros and a knowledge of their basic shape.