Do Now
Make a table for –2 ≤ x ≤ 2 and draw the
graph of:
y=
x+1
2
+3
(Problem #1 from today’s packet)
6
4
2
-10
-5
5
-2
-4
-6
10
Absolute Value Functions
Absolute value functions are functions that
contain absolute value in their equations.
The most basic absolute value function is:
y = |x|
First We’ll Graph a Similar Equation…
The line y = x
6
4
2
-5
5
-2
-4
-6
Let’s Compare Tables
y=x
x
-3
-2
-1
0
1
2
3
y
-3
-2
-1
0
1
2
3
y = |x|
x
-3
-2
-1
0
1
2
3
y = |x|
y
Let’s See What Happens On The Graph
6
4
2
-5
5
-2
-4
-6
Adding a Coefficient Inside
y = |x|
x
-3
-2
-1
0
1
2
3
y
3
2
1
0
1
2
3
y = |2x|
x
-3
-2
-1
0
1
2
3
y = |2x|
y
6
4
2
-5
5
-2
-4
-6
The graph gets steeper on both sides and closer to its line of symmetry.
In Your Calculator
Let’s look at:
y = |4x|
y=|
1
2
x|
y = |– 2x|
y = |2x|
x
-3
-2
-1
0
1
2
3
y
6
4
2
0
2
4
6
y = |– 2x|
x
-3
-2
-1
0
1
2
3
y = |– 2x|
y
The graph of the absolute value function
takes the shape of a V.
What are some observations that
you can make about these graphs?
1. As the coefficient of x gets larger, the graph becomes
steeper, closer to its line of symmetry.
2. As the coefficient of x gets smaller, the graph
becomes less steep, further from its line of symmetry.
3. If the coefficient of x is negative, the graph is the
same as if that coefficient were positive. Absolute value
changes negative values to positive values.
Notice that the graphs of these absolute value
functions are on or above the x-axis. Absolute
value always yields answers which are positive or zero.
In Your Calculator
Let’s look at:
y = |x| + 3
y = |x| – 5
Challenge
See if you can shift the graph right or left by
adding or subtracting a number from
somewhere else in the equation.
y = |x + 3|
y = |x – 5|
Summary
Adding or subtracting a number outside the
absolute value shifts the graph up or down.
Adding or subtracting a number inside the
absolute value shifts the graph right or left.