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
SWBAT… graph absolute value functions
Agenda 1. Absolute value review (10 min)2. Review problem from Friday (5 min)3. Review HW#1/#2 (15 min)4. Graphing absolute value functions (10 min)5. Transformations of absolute value functions (5 min)
HW#3: Absolute value functions and
HW#4: Linear graphs & table of values application (due Wed)
Mon, 9/19
Test Corrections: Common spelling/ grammar mistakes1. “I” should be capitalized
2. “supposed to” not suppose to1. “Suppose” is a verb, meaning to think or to ponder.
2. The correct way to express a duty is to write, “I was supposed to…”
3. It’s “plugged” not pluged
4. It’s “parenthesis”
5. It’s “going to” not gonna1. Even worse is “imma gonna”
6. Your vs. you’re
7. Their vs. there1. “Their” is possessive; “there” refers to distance; and “they’re” is a
contraction of “they are.”
We have begun a new unit on functions: Cell phone project
We will be able to:
1. Know the Cartesian Coordinate System (HW1)
2. Graph linear functions (equations) using a table of values (HW2)
3. Graph absolute value functions (HW3)
4. Interpret real life graphing examples (HW4)
5. Graph piecewise value functions (HW5)
6. Write and identify linear functions (HW6)
7. Write algebraic equations given various forms of data (HW7)
8. List the domain and range of a function (HW8)
9. Determine if a relation is a function using the vertical line test or given a diagram (HW8)
10. Evaluate a function and write as an ordered pair (HW8)
Ex 2: Graph x – 2y = 5 using a table of valuesFirst Step: Solve for y (write y as a function of x)
x – 2y = 5
–2y = -x + 5
2
5–x
2
1y
y
x
Second Step: Make a Table of Values
x y (x, y)
-2 -3.5 (-2, -3.5)
-1 -3 (-1, -3)
0 -2.5 (0, -2.5)
1 -2 (1, -2)
2 -1.5 (2, -1.5)
2
5–x
2
1
2
5–(-2)
2
1
2
5–(-1)
2
1
2
5–(0)
2
1
2
5–(1)
2
1
2
5–(2)
2
1
2
5–x
2
1y
SWBAT… graph absolute value functions
Agenda 1. Warm Up (5 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 + 1 compare to the parent function graph, y = x?
HW#3-Absolute value functions and HW#4-Linear graphs & table of values application
Tues, 9/20
The graph of the function y = x + 1 shifts 1 units up from the parent function, y = x.
Q: How does the graph of y = -x – 2 compare to the parent function graph, y = x?
A: The graph of the function y = -x – 2 is reflected across the x-axis and shifts 2 units down from the parent function, y = x.
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: A function in the form y = |mx + b| + c (m 0)
Ex 1: Graph y = |x| by completing a table of values:
Parent Function
|-1|
|0|
|1|
|2|
Ex 2: Graph y = |x| – 3 by completing a table of values:
x y-2 -1 0 1 2
y =|-2| – 3= -1 y =|-1| – 3= -2 y =|0| – 3= -3 y =|1| – 3= -2 y =|2| – 3= -1
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|
Q: How would y = |x| + 5 transform from the parent function, y = |x|?
A: The function y = |x| + 5 would shift 5 units up from the parent function, y = |x|.
Reminders!
1. More absolute value examples on-line
2. HW3-Absolute value functions
3. HW4-Tables of values application
4. Review PPT3-Piecewise functions
Tomorrow for 3rd period go to the Distance Learning Lab (next to the clinic)
SWBAT… graph absolute value functionsAgenda 1. Warm Up (10 min)2. Absolute value functions (20 min)3. Applications of TOV (15 min)
Warm-Up:
1. -|x + 1| = ? if x = -2, x = -1, x = 0, x = 1, x = 2 2. How does the graph of y = |x + 1| compare
to the parent function graph, y = x?(It does NOT shift up 1 unit!)
3. How does the graph of y = -|x + 1| compare to the parent function graph, y = x?
Review PPT4 : Algebraic equations from data
Thurs, 9/21
Warm-Up: #2
The graph of y = |x + 1| is shifted one unit to the left.
2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
y = -|x + 1|
The vertex, or maximum point, is (-1, 0).
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
y = -|x + 1| is shifted 1 unit to the left and rotated around the x-axis from the parent function, y = |x|
Problem #3 y =
SB
2x
2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
y=|x – 2| – 1
The vertex, or minimum point, is (2, -1).
Ex 3: 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
y = |x – 2| – 1 is shifted 2 units to the right and 1 unit down from the parent function, y = |x|
Q: How would y = |x + 4| + 3 transform from the parent function, y = |x|?
A: The function y = |x + 4| + 3 would shift 4 units to the left and 3 units up from the parent function, y = |x|.
#6 on HW3
Q: How would y = -|x + 1| + 3 transform from the parent function, y = |x|?
A: The function 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, y = |x|.
