Draw a graph of the mirror line y=x, the function f:x 3x+2 and its inverse f`1 x x-2/3, for the domain of x, -2<x<8

x -2 0 4 8
y=x -2 0 4 8
These numbers were given to me what i want to know is why 0 and 4 and how do i come up with the numbers on my own for future questions??

The choice of x vales to use depends very much on the question and what you are asked to show. It is quite usual to calculate the value for x=0. In this case where the function is a straight line you only really need to have values for x=-2 and x=8 and then draw the straight line between them.

Where the function is not a straight line then having several values helps to construct the line. It is usual to have both +ve and - values of x.

The question requires you to graph the three functions. The x-values given are suggested values, as explained by Dr. Russ.

Plot the functions graphically and you will be able to make observations and remarks.
Here's my version of the graph:
http://i263.photobucket.com/albums/ii157/mathmate/trina.png

To plot the graphs accurately, you need to evaluate the function f(x) = 3x + 2 and its inverse f^(-1)(x) = (x-2)/3 over the given domain -2 < x < 8.

Let's start by substituting the x-values from the domain into the function f(x) = 3x + 2:

For x = -2:
f(-2) = 3(-2) + 2 = -6 + 2 = -4

For x = 0:
f(0) = 3(0) + 2 = 0 + 2 = 2

For x = 4:
f(4) = 3(4) + 2 = 12 + 2 = 14

For x = 8:
f(8) = 3(8) + 2 = 24 + 2 = 26

Now, let's substitute the x-values from the domain into the inverse function f^(-1)(x) = (x-2)/3:

For x = -2:
f^(-1)(-2) = (-2 - 2)/3 = -4/3

For x = 0:
f^(-1)(0) = (0 - 2)/3 = -2/3

For x = 4:
f^(-1)(4) = (4 - 2)/3 = 2/3

For x = 8:
f^(-1)(8) = (8 - 2)/3 = 6/3 = 2

Now, you have the corresponding y-values for the function f(x) = 3x + 2 and its inverse f^(-1)(x) = (x-2)/3 for the given domain.

To plot the graph, you can use a coordinate system with the x-axis and y-axis labeled. Plot the points corresponding to each value of x and y obtained above.

For example, plot the points (-2, -4), (0, 2), (4, 14), and (8, 26) for the function f(x) = 3x + 2. And plot the points (-2, -4/3), (0, -2/3), (4, 2/3), and (8, 2) for the inverse function f^(-1)(x) = (x-2)/3.

After plotting all the points, you can connect them using a smooth line to represent the graph of each function. The line y = x represents the mirror line, and you can include it as well.