Transcript NOTES Absolute Value Functions

Warm Up/Do Now
Solve the following:
Numbers 1-5 are all
equal to positive
numbers once the
absolute value bars
are alone.
Why is this? What
would happen if they
were equal to
negative numbers?
Absolute Value
Functions
Chapter 2
Warm Up/ Do Now
Solve & Graph Solution on a Number Line
①
| 2x + 3 | < 6
④
| x | + 4 < 12
②
| 2x – 3 | > 5
⑤
-3 + | x – 2 | > 5
③
| 10 + 4x | < 14
⑥
| x + 1| < -6
Solve the following:
| x + 2 |< -1
NO SOLTUION!!!!
Absolute values always
end up positive so there
is no way the absolute
value of |x+2| could be
less than negative 1.
Solve the following:
| x + 2 |< -1
NO SOLTUION!!!!
Absolute values always
end up positive so there
is no way the absolute
value of |x+2| could be
less than negative 1.
Solve the following:
| x - 2 |> -3
ALL REAL
NUMBERS!!!!
Absolute values are
always greater than any
negative number!
Parent Function:
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f(x) = |x|
V-shape
It is symmetric about the y-axis
The vertex is (0,0)
Doman: (-∞, ∞)
Range: [0, ∞)
The Absolute Value Function
The graph of
f(x) = a|x – h| + k
is the graph of y = |x|
translated h horizontal
units and k vertical units
and stretched by a.
• The new vertex is at (h, k)
IF the equation has +h you need to make it a negative in the vertex!!!
When k is on the right, you keep its sign!
Graphing Absolute Value Functions
y = a|x – h| + k
1.Plot the vertex (h, k)
2.Use the a value as slope to plot points on
the right side
3.Use symmetry to find corresponding point
on the left side
4.Connect the dots in a V-shape
Remember:
If a is positive if the graph goes up
If a is negative if the graph goes down
Graph f(x) = 3|x + 4|
1. Plot the vertex
2. Use a as a slope to move left & right
vertex = (-4, 0)
a=3
Finding an Equation from a Graph
Find the vertex coordinate
(1, -4) so h is 1 and k is -4
Find a by counting the
slope from the vertex to
another point to the right
slope = 2/1 so a is 2
So the equation is:
y = 2|x – 1| - 4
Plug h, k, and a into
y = a|x – h| + k
Write the equation for:
y = -|x +2| + 3
Real Life!
Lets graph it in a calculator!
Exit Slip
• You will be handed an exit slip.
• Complete it without using any notes
or asking for help.
• Once finished, bring it to me to be
checked.
• Good luck!