Download L6 Absolute value functions

Integrated Algebra
NOTES: Absolute Value Functions



Name
Absolute value functions are functions that result in a “v” .
Their equations have “x” inside an absolute value sign.
They can be graphed with a table of values.
Each of these functions results in a line:
y = x4
f(x) = -5 2 x
g(x) = 3x + 1
……they all have “x” inside the absolute value sign.
To graph an absolute value function, use a table of values.
Graph the function : f(x) = 2 x
Set up a table of values
x
y
-2
-1
0
1
2
4
2
0
2
4
Integrated Algebra
SETTING UP THE TABLE OF VALUES
Be careful when setting up a table for these graphs. Sometimes the
standard –2 to 2 will not be enough to show the “V” shape, and someone
looking at the graph without seeing the equation may think they are looking at
a linear equation.
Graph f(x) = x  3
x
y
-2
-1
0
1
2
5
4
3
2
1
When setting up the table, follow these steps:
f(x) = x  3
1. Set expression inside the absolute value
sign = 0
x–3=0
+3
+3
x=3
2. Solve the equation, the answer is the
middle number in your table.
x
f(x)
1
2
2
1
0
1
2
3
4
5
3. Go 2 numbers away in both directions to
finish the table.
4. Find the corresponding f(x) values, graph.
Integrated Algebra
TRY: Graph each absolute value function:
1.
f(x) = x  1
2.
f(x) = x + 3
3.
f(x) = - x  2
Integrated Algebra
HOMEWORK: Graphing absolute value functions
Name
You will need your own sheet of graph paper for this assignment. Please put
two graphs per side of a page.
Graph each absolute value function. Graph only one function on each set of
axes.
1. f(x) = x  3
2. f(x) =
3. f(x) = - x  5
4.
x
f(x) = x - 2