, Absolute values
definition
If x = 0 - /Tl 1
eg) 1 21 2 ey) 1-21- follow
· = -
=
x]2
E
·
if x20 0 1T)) = -
Th (x -
2) If /
-
220 (positives
,
(x-2) If <- 20 12/2 (negativel
-
,
*
will - distance from o
b 17-al " distance of i from a
Equations : Form latbl =
c
3
·
If <O - no solution
·
if ( =
0 >
- I solution Isolate absolute values
·
If (10 +
2 solutions
eg)(x
↳ ey) l=%=
-
11 =
3
CC0 : 2 solutions
x =
3 or 1 = 3
-
1 x
-
-
x =
4 x = -
2
y
*
factonse if you can ! ie . -50 =
14 or 22 -
50 = -
14
2
x2 -
64 = 8 x
-
36 =
0
Absolute value function
y
= a(x -
p) +
q
*
big number skinny
shape a = -
·
-
a
↳ a small number a sleep
(p ; q) turning point
=
↓
·
-
a = 0
equation symmetry
-
·
x =
p - for axls or
*
a shifts graph up and down
right
·
p-shifts graph left and
↓
↓ left v + - down
b
-
↳ right --
+ 0
up
Absolute value functions
skerching
aso v
shape - =
-
928 = n
*
calculator work
-into ↳ table mode !
intercepts - let y
=
0
letx
y-int
·
- = 0
turning points <piq) ' opposite sign than in
axis of
symmetry - If (p = 0) than axis is ( = 0
*
remember :
always label axis
,
graph t
turning points
, Finding the equation of the
graph
Method 1 :
Method 2 :
↳ [
determine turning point ep ; q) a =
q y
-
↳ look for i
+y values to substitute p x)
-
↳
find a to complete
Absolute values Inequalities
inequalitytype :
1)(x]
230 : -
((T((
20 :
no solution
2) 13137 -
230 : < >C or < -C
↳ 00 : roue for all real numbers
* when restrict the denominator has an
working fractions it in
with -
*
inequalities are always on the left !
↳
312 7 + 3
-
13 + /
3 = 213 + 7)
2) 3 + (133 etc .
*
If there is a variable on RHS - restrict it
b 13-2x) > + 22 + 11G
ey .
x ? -1
below
number line including everything above and the restrictions
↓
Draw a
↓ look values where in restriction
for overlaps 12. no + an answer .
Solving Absolute values
using Graphs
(g) 1x 3) = 2 2) skerch graphs
-
y = (x
-
3)
2 A
1) Solve :
y
:
x 3 2 7) 3
=
= 2
-
- -
3
x = 5 1 S : V 2
x =
y >
1 : Int
yint ! i
3 5
x 3 10 3) I
-
=
0 =
y
-
x =
3 1 3)
y
= -
3
y
=
T : (0 ; 3)
3) check for points unar overlap
(below graph 2)
11 (15
·
nore : If variable on RHS >
- restrict + make sure it's not included
definition
If x = 0 - /Tl 1
eg) 1 21 2 ey) 1-21- follow
· = -
=
x]2
E
·
if x20 0 1T)) = -
Th (x -
2) If /
-
220 (positives
,
(x-2) If <- 20 12/2 (negativel
-
,
*
will - distance from o
b 17-al " distance of i from a
Equations : Form latbl =
c
3
·
If <O - no solution
·
if ( =
0 >
- I solution Isolate absolute values
·
If (10 +
2 solutions
eg)(x
↳ ey) l=%=
-
11 =
3
CC0 : 2 solutions
x =
3 or 1 = 3
-
1 x
-
-
x =
4 x = -
2
y
*
factonse if you can ! ie . -50 =
14 or 22 -
50 = -
14
2
x2 -
64 = 8 x
-
36 =
0
Absolute value function
y
= a(x -
p) +
q
*
big number skinny
shape a = -
·
-
a
↳ a small number a sleep
(p ; q) turning point
=
↓
·
-
a = 0
equation symmetry
-
·
x =
p - for axls or
*
a shifts graph up and down
right
·
p-shifts graph left and
↓
↓ left v + - down
b
-
↳ right --
+ 0
up
Absolute value functions
skerching
aso v
shape - =
-
928 = n
*
calculator work
-into ↳ table mode !
intercepts - let y
=
0
letx
y-int
·
- = 0
turning points <piq) ' opposite sign than in
axis of
symmetry - If (p = 0) than axis is ( = 0
*
remember :
always label axis
,
graph t
turning points
, Finding the equation of the
graph
Method 1 :
Method 2 :
↳ [
determine turning point ep ; q) a =
q y
-
↳ look for i
+y values to substitute p x)
-
↳
find a to complete
Absolute values Inequalities
inequalitytype :
1)(x]
230 : -
((T((
20 :
no solution
2) 13137 -
230 : < >C or < -C
↳ 00 : roue for all real numbers
* when restrict the denominator has an
working fractions it in
with -
*
inequalities are always on the left !
↳
312 7 + 3
-
13 + /
3 = 213 + 7)
2) 3 + (133 etc .
*
If there is a variable on RHS - restrict it
b 13-2x) > + 22 + 11G
ey .
x ? -1
below
number line including everything above and the restrictions
↓
Draw a
↓ look values where in restriction
for overlaps 12. no + an answer .
Solving Absolute values
using Graphs
(g) 1x 3) = 2 2) skerch graphs
-
y = (x
-
3)
2 A
1) Solve :
y
:
x 3 2 7) 3
=
= 2
-
- -
3
x = 5 1 S : V 2
x =
y >
1 : Int
yint ! i
3 5
x 3 10 3) I
-
=
0 =
y
-
x =
3 1 3)
y
= -
3
y
=
T : (0 ; 3)
3) check for points unar overlap
(below graph 2)
11 (15
·
nore : If variable on RHS >
- restrict + make sure it's not included
