Absolute Value Function

Hello fellow classmates! This is Paulene :D Yesterday, we learned what an Absolute Value Function is and how to graph it.

This is the Parent Graph of all absolute value functions or "Basic Shape" f(x) = |x|

It has the same V-shape, but they can be wider or narrower. They might have their vertex somewhere else other than the origin, and they might open downward instead of upward.



Shifted Shape: f(x) = |x-h| + k :: You read k as is and h as opposite.

How to graph by "reading" an Absolute Value function:
1. Read k values as is. If k is positive, the graph shifts up.
If k is negative, the graph shifts down.
2. Read h values as opposite. If h is positive, the graph shifts left.
If h is negative, the graph shifts right.

Eg. (f)x = |x+1| + 2 :: The graph will shift 2 up, 1 to the left.

How to graph an Absolute Value Function using a table:

1. Choose an x-value
2. Sub in the value for x in the equation
3. Simplify
4. The answer is the now the y-value
5. Repeat Steps 1-4 for 2-4 more x-values and sketch the function.

Eg. (f)x = |x+2|

x value - y value

0 - |0+2| = 2
1 - |1+2| = 3
2 - |2+2| = 4
-1 - |-1+2| = 3
-2 - |-2+2| = 0