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
Sketch the graph of the following functions. State the zeros of the function and the x-intercepts of the graph. Describe the shape of each graph. Do not use graphing technology other than as a check of your work.
1. f(x) = 4 2. f(x) = 0 3. f(x) = 
x
4. f(x) = 2x - 1 5. f(x) = - x + 4 6. f(x) = (x - 4)(x + 2)
7. f(x) = 2(x - 4)(x + 2) 8. f(x) = - 2(x - 4)(x + 2) 9. (x - 4)(x + 2)
10. f(x) = x2 - 2x - 3 11. f(x) = 2x2 + 7x + 3 12. f(x) = - 2x2 + x + 3
Students will be expected to:
- Recognize and draw basic graphs of polynomial functions to degree 4.
- Use graphs to obtain precise polynomial functions.
Introduction
This section consists of three lessons as follows:
Lesson 01 Graphs of Constant, Linear, and Quadratic Functions
This lesson approaches the graphing of constant, linear, and quadratic functions from the point of view of the zeros of the function. The zeros of the function are used to plot the x-intercepts of the graph and then a knowledge of the "basic shape" of the graph is used to sketch the graph. One or more other points are also used to make the sketch a little more accurate.
Lesson 02 Graphs of Cubic and Quartic Functions
This lesson approaches the graphing of cubic and quartic functions from the point of view of the zeros of the function. The zeros of the function are used to plot the x-intercepts of the graph and then a knowledge of the "basic shape" of the graph is used to sketch the graph. One or more other points are also used to make the sketch a little more accurate.
Lesson 03 Using Graphs to Obtain Functional Notation
The graph is used to determine the zeros of the function. The zeros are then used to write the function in factored form. The value of the leading coefficient is determined by substituting in one other point on the graph.
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.