SWBAT

1
SWBAT graph absolute value functions
Wed, 10/10

• Agenda
• WU (10 min)
• Transformations of linear functions (5 min)
• Absolute value functions (20 min)
• Transformations of absolute value functions (10
  min)
• Warm-Up
• How does the graph of y x 2 compare to the
  parent function graph, y x?
• HW3-Absolute value functions

2
Absolute Value Review

• 5.) -x ? if x -2
• Answer 2
• 6.) x - 3 ? if x -2
• Answer -1
• 7.) x - 2 - 1 ? if x -2
• Answer 3
• 8.) -x 1 ? if x -2
• Answer -1

• 1.) 5 ?
• Answer 5
• 2.) -5 ?
• Answer 5
• 3.) -10 ?
• Answer 10
• 4.) 0 ?
• Answer 0

3
Absolute Value Function
Ex 1 Graph y x by completing a table of
values
Parent Function
x y (x, y)
-2 2 (-2, 2)
-1 1 (-1, 1)
0 0 (0, 0)
1 1 (1, 1)
2 2 (2, 2)
4
(HW3, Problem 2 and 2a)
How would the graph of y x 1 transform from
the parent function graph, y x The graph of y
x 1 would shift one unit to the left from
the parent function, y x.

• Ex 3 Graph y x 1 by completing a table of
  values

x y (x, y)
-2 1 (-2, 1)
-1 0 (-1, 0)
0 1 (0, 1)
1 2 (1, 2)
2 3 (2, 3)
5
(HW3, Problem 3 and 3a)
How would the graph of y x 2 transform from
the parent function graph, y x The graph of y
x 2 would shift two units to the right from
the parent function, y x.

• Ex 3 Graph y x 2 by completing a table of
  values

x y (x, y)
-2 4 (-2, 4)
-1 3 (-1, 3)
0 2 (0, 2)
1 1 (1, 1)
2 0 (2, 0)
3 1 (3, 1)
6
(HW3, Problem 4 and 4a)
How would the graph of y -x transform from
the parent function graph, y x The graph of y
-x would rotate around the x-axis from the
parent function, y x.

• Ex 3 Graph y -x by completing a table of
  values

x y (x, y)
-2 -2 (-2, -2)
-1 -1 (-1, -1)
0 0 (0, 0)
1 -1 (1, -1)
2 0 (2, -2)
7
(HW3, Problem 5 and 5a)
How would the graph of y -x 1 transform
from the parent function graph, y x? y -x
1 is shifted 1 unit to the left and rotated
around the x-axis from the parent function, y
x
Ex 4 Graph y -x 1 by completing a table
of values
y --2 1 -1 y --1 1 0 y -0 1
-1 y -1 1 -2 y -2 1 -3
8
How does the graph of y x 3 transform from
the parent function graph of y x ? y x
3 is shifted 3 units down from the parent
function, y x

• Ex 2 Graph y x 3 by completing a table of
  values

x y (x, y)
-2 -1 (-2, -1)
-1 -2 (-1, -2)
0 -3 (0, -3)
1 -2 (1, -2)
2 -1 (2, -1)
9

• Q How would the graph of y x 5 transform
  from the parent function graph, y x?
• A The graph of y x 5 would shift 5 units
  up from the parent function, y x.

10
HW3, Problem 6

• 5. Q How would the graph of y -x 1 3
  transform from the parent function, y x?
• A The graph of y -x 1 3 would shift 1
  unit to the left shift, 3 units up, and rotate
  around the x-axis from the parent function graph,
  y x.

11
How would the graph of y x 2 1 transform
from the parent function graph, y x? y x
2 1 is shifted 2 units to the right and 1 unit
down from the parent function, y x
Ex 5 Graph y x 2 1 by completing a
table of values
y -2 2 1 3 y -1 2 1 2 y 0
2 1 1 y 1 2 1 0 y 2 2 1 -1