The function functions
modulus is also known as the absolute value
Sketching the modulus
of linear
y = 1) (y = mod/modulus (C or absoc (
4 Y ·
tells us the magnitude ofc. absolute value of think about
completing the square to find vertex
·
modulus graphs have like a parabola a vertex
I-21 -> all positive 2 and line
of
outputs =
symmetry
.
131 -
> 3
D y
= (x-31 (3 01 ,
② y = (x -
31 -
3
x 2 1012 (3 3) x g
y 3 C
-
=
x= 0
+
y =
-
= ,
Y 21012 , 3)
10
I lin
L
(x)
y =
I
3
X --
(3 , 0)
!
10 , 01
,
I
O
X
3
-13 -3)
-
.
③ y = 12x + 101
Dy = 2(x + S
↓ Vertex (-5 , 0 ⑤ y = 110-2x
reflected up the s axis & translation of graph
+ 18 = -
10 = ( -
10 , 0 ① y = 1 -
1) 10 + 2x))
-
x2 = =2 = ( -
S, 0) =
Vertex y =12x 101 -
③ y = 12) + 10/ 2x = 10
2x = -
10 (= S (S , 0)
x =
- S
C 5 , 0)-
② translation of graph
1 101
y = 2x +
-
+ 10 = - 10 = (-1
(O , 10) xz = =
2 = ( S
-
-=
reflection in y
co
Examples of sketching the modrius
of linear functions
Dy = ( + 7) ② y= 13x -
6) ③ y = 12- x ⑪ y
C 7,-
0) (2 , 0) =
y = (x -
2) =
- (0 ,6)
(2 , 0)
.
(7 , 6) ~
~ O
X
C -
7 01
~
,
O
this only flips
I
-
③ y = (x) + 2 ⑳ y
= (x +Sl -
3 ⑦ y
= s -
x + 10) modulus g
( S, 3) (x+ 101 + S 2 like a
y
- - -
C-10 , 8) x =
1
-
m =- M=
(-10 , 8)
I
X (0 , 2) Y
3 3 (0 , 2)
,
modulus is also known as the absolute value
Sketching the modulus
of linear
y = 1) (y = mod/modulus (C or absoc (
4 Y ·
tells us the magnitude ofc. absolute value of think about
completing the square to find vertex
·
modulus graphs have like a parabola a vertex
I-21 -> all positive 2 and line
of
outputs =
symmetry
.
131 -
> 3
D y
= (x-31 (3 01 ,
② y = (x -
31 -
3
x 2 1012 (3 3) x g
y 3 C
-
=
x= 0
+
y =
-
= ,
Y 21012 , 3)
10
I lin
L
(x)
y =
I
3
X --
(3 , 0)
!
10 , 01
,
I
O
X
3
-13 -3)
-
.
③ y = 12x + 101
Dy = 2(x + S
↓ Vertex (-5 , 0 ⑤ y = 110-2x
reflected up the s axis & translation of graph
+ 18 = -
10 = ( -
10 , 0 ① y = 1 -
1) 10 + 2x))
-
x2 = =2 = ( -
S, 0) =
Vertex y =12x 101 -
③ y = 12) + 10/ 2x = 10
2x = -
10 (= S (S , 0)
x =
- S
C 5 , 0)-
② translation of graph
1 101
y = 2x +
-
+ 10 = - 10 = (-1
(O , 10) xz = =
2 = ( S
-
-=
reflection in y
co
Examples of sketching the modrius
of linear functions
Dy = ( + 7) ② y= 13x -
6) ③ y = 12- x ⑪ y
C 7,-
0) (2 , 0) =
y = (x -
2) =
- (0 ,6)
(2 , 0)
.
(7 , 6) ~
~ O
X
C -
7 01
~
,
O
this only flips
I
-
③ y = (x) + 2 ⑳ y
= (x +Sl -
3 ⑦ y
= s -
x + 10) modulus g
( S, 3) (x+ 101 + S 2 like a
y
- - -
C-10 , 8) x =
1
-
m =- M=
(-10 , 8)
I
X (0 , 2) Y
3 3 (0 , 2)
,
