Unit+7+Journal+Responses

__** Unit 7: Nth Root Functions and Inverses **__

**__ 7.1: __**
A.) Using the link below, graph the following two equations on the same coordinate plane. [|Graphing Tool]

f(x) = (1/2)x+4 g(x) = 2x-8

Find f(2) = Find g(5) =

Find f(12) = Find g(10) =

List your findings in your online journal as coordinate points. (Double check that these points are on the correct function on your graph.) And explain what you notice about your calculations for function "f" and function "g".

B.) Using the same link as above, graph the following two equations on the same coordinate plane.

f(x) = x^2 + 2 g(x) = sqrt(x-2)

Find f(2) = Find g(6) =

Find f(11) = Find g(3) =

List your findings in your online journal as coordinate points. (Double check that these points are on the correct function on your graph.) And explain what you notice about your calculations for function "f" and function "g".

C.) Make your best argument for why any negative x-value will not be included in the domain of the function g(x).

**__ 7.2: __**
Summarize the relationship between inverse functions in your online journal by answering the following questions:
 * Given one graph, explain the process you would use to graph its inverse.
 * What is the relationship between the graphical representations?
 * Given an equation, explain the process you would use to find its inverse equation.
 * Given a table of values for a function, explain how you would create a table of values that would represent the inverse function.

**__ 7.3: __**
Using the same graphing program from journal 7.1, graph the following 2 equations on the same coordinate plane. f(x) = x^2 - 3 g(x) = sqrt(x+3)

Notice how the two graphs are not truly symmetrical. (One parabola has 2 sides and the other only has one side.) Explain in your online journal why the "sideways" parabola only has one side.


 * In order to make this true, the square root graph has a limited domain and range.**


 * Looking at the original parabola, which side would need to be erased to make these two graphs truly symmetrical? Write a response in your online journal.
 * How would you need to modify the domain or range of the quadratic function (the original parabola), so that it becomes the true inverse of the square root function (where they are symmetrical - each having only half of the parabola)?

__** 7.4: **__
Look at the following document which contains an example that has been worked out. You will find this document below. Explain in full sentences each step that was taken in the problem and why that step was chosen. Be clear about the step you are looking at, for example "going from line 1 to line 2, ..." Be sure to complete the challenge question at the bottom - it is not optional. (This should all be written in your online journal.)