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
Find the inverse of the functions in exercises 1 to 5 below:
1. f(x) = 4x2
2. f(x) = -2(x - 4)2
3. f(x) = 
4. f(x) = x2 + 6x + 9
5. f(x) = x2 - 8x + 1
6. The inverses of the functions in 1 to 5 above are not functions. Give a restriction on the domain of f so that its inverse will be a function.
7. Using the restricted domain, graph each f and the corresponding 
on the same set of axes.
Prerequisites
To be successful in this lesson, it would be helpful to know the following:
- The definition of a quadratic function.
- The definition of and how to find the domain and range of a quadratic function.
- The various methods of describing a function, viz. "f of x" notation, "y = " notation, and graphing.
- How to rearrange a formula to solve for any given variable.
- How to substitute one expression or formula into a second expression or formula.
- How to draw the graph of a quadratic function.
- The definition of an inverse function.
- How to solve quadratic equations.