I think I am a little bit confused with this absolute value thing. When do I change the sign inside? Example f(-2)= |-2-2|. Is this equal to -4 or do I need to change a sign inside the absolute value when adding. I am trying to get some x and y values to graph. Thanks for any help you can give me.

evaluate the expression inside the || and then throw away any negative sign.

|-2-2| = |-4| = 4
|3+5-10| = |-2| = 2

if f(x) = |x-2|
then f(-2) = |-2-2| = 4
f(10) = |10-2| = 8
f(-5) = |-5-2| = |-7| = 7

Thank you so much Steve. Now I see the light.

To understand when to change the sign inside the absolute value, let's examine the definition of the absolute value function.

The absolute value function, denoted as |x|, returns the magnitude or distance of a number from zero on a number line. Therefore, it always gives a non-negative value.

In your example, you are given f(-2) = |-2-2|. To simplify this expression, you start by evaluating what is inside the absolute value, which is -2 - 2 = -4.

Now, since the absolute value function always gives a non-negative value, you need to take the absolute value of -4, which is 4. Therefore, f(-2) = |4| = 4.

To clarify, you do not change the sign inside the absolute value when adding. The absolute value function only cares about the magnitude or distance from zero and disregards the sign.

When graphing a function that involves absolute values, there are a few steps you can follow:

1. Identify all the critical points where the absolute value function changes behavior. In your case, this occurs when the expression inside the absolute value crosses zero.

2. Evaluate the function for values of x on both sides of these critical points, using both positive and negative values. This will help you determine the behavior of the function on each side of the critical points.

3. Plot the resulting points on a graph, connecting them smoothly to draw the graph of the absolute value function.

Remember, when graphing absolute value functions, the graph typically resembles a "V" shape centered at the critical point.