Download 6.5 Solving Open Sentences involving Absolute Value

6.5 Solving Open Sentences
involving Absolute Value
 Remember the
absolute value is the
distance from zero on
 |x – 4| = 5
 Write the equation without
the absolute values and
a number line.
then again with the other
sign after the =.
 Absolute value means
you are going to have  x – 4 = 5 OR x – 4 = -5
2 equations!
 Solve.
 The expression inside  x = 9 or x = -1
the absolute value
 Solution is {-1,9}
symbols is either
positive or negative.
Try These
 Solve |b + 6| = 3
 {-9, –3}
 You may get the answer
and be asked for the
equation!
-4
1
6
 Find the middle between
the 2 numbers.
1
 How many spaces did
you move to get there?
5
 Plug that information into
an equation:
 |x – middle| = spaces you
moved to get there
 |x – 1| = 5
Try this one
 Write the equation for this graph.
7
12
17
 What is the middle #?
 12
 How many spaces did you move to get there?
5
 Plug it into the equation
 |x – 12| = 5
Graphing absolute value functions
 An absolute value function is a function written
as f(x) = |x| when f(x) > 0 for all values of x.
 It’s sometimes known as a piecewise function: a
function that can be written using two or more
“pieces” or expressions.
 Think V for Value!!!
 x if x  0
f ( x)  
 x if x  0
Try This One
Graph f(x) = |x – 4|
Set x – 4 = 0
x = 4
The V-point is @ (4,0)
Slope is 1 to the right of (4,0)
(positive) x - 4
Slope is –1 to left of (4,0)
(negative) –x + 4
Homework
p. 325 1-6. Check them with me before
you begin your homework.
#42 p. 325 7-35 odd, 47, 49-51