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Wed, 10/10. SWBAT… graph absolute value functions. Agenda WU (10 min) Transformations of linear functions (5 min) Absolute value functions (20 min) Transformations of absolute value functions (10 min) Warm-Up: - PowerPoint PPT Presentation
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SWBAT… graph absolute value functions
Agenda 1. WU (10 min)2. Transformations of linear functions (5 min)3. Absolute value functions (20 min)4. 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?
HW#3-Absolute value functions
Wed, 10/10
Absolute Value Review1.) |5| = ?Answer: 5
2.) |-5| = ?Answer: 5
3.) |-10| = ?Answer: 10
4.) |0| = ?Answer: 0
5.) |-x| = ? if x = -2Answer: 2
6.) |x| - 3 = ? if x = -2Answer: -1
7.) |x - 2| - 1 = ? if x = -2Answer: 3
8.) -|x + 1| = ? if x = -2Answer: -1
x y (x, y) -2 2 (-2, 2)
-1 1 (-1, 1)
0 0 (0, 0)
1 1 (1, 1)
2 2 (2, 2)
|x| |-2|
2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
Absolute Value Function
Ex 1: Graph y = |x| by completing a table of values:
Parent Function
|-1|
|0|
|1|
|2|
Ex 3: Graph y = |x + 1| by completing a table of values:
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|.
(HW#3, Problem #2 and #2a)
x y (x, y)
-2 1 (-2, 1)
-1 0 (-1, 0)
0 1 (0, 1)
1 2 (1, 2)
2 3 (2, 3)
|1x| |1-2| |1-1| |10| |11|
|12|
2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
Ex 3: Graph y = |x – 2| by completing a table of values:
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|.
(HW#3, Problem #3 and #3a)
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)
|2x| |2-2| |2--1|
|20| |21| |22|
2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
|23|
Ex 3: Graph y = -|x| by completing a table of values:
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|.
(HW#3, Problem #4 and #4a)
x y (x, y)
-2 -2 (-2, -2)
-1 -1 (-1, -1)
0 0 (0, 0)
1 -1 (1, -1)
2 0 (2, -2)
|x|- |-2|- |-1|-
|0|-
|1|- |2|-
2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
y = -|x + 1|
Ex 4: Graph y = -|x + 1| by completing a table of values:
x y-2 -1 0 1 2
y =-|-2 +1| = -1 y =-|-1+ 1| = 0 y =-|0 + 1| = -1 y =-|1 +1| = -2 y =-|2 +1| = -3
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|
(HW#3, Problem #5 and #5a)
Ex 2: Graph y = |x| – 3 by completing a table of values:
2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
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|
x y (x, y)
-2 -1 (-2, -1)
-1 -2 (-1, -2)
0 -3 (0, -3)
1 -2 (1, -2)
2 -1 (2, -1)
3- |x|3- |-2|3- |-1|
3- |0|
3- |1|
3- |2|
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|.
HW#3, 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|.
2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
y=|x – 2| – 1
Ex 5: Graph y = |x – 2| – 1 by completing a table of values:
x y-2 -1 0 1 2
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
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|
