Module 2

Monday Tuesday Wednesday Thursday Friday

29 30 31 September 1 2
2.1 Graphing Absolute Student Holiday/
Value Functions
Staff Development

5 6 7 8 9
2.1 Graphing Absolute 2.2 Solving Absolute 2.2 Solving Absolute 2.3 Solving Absolute
Labor Day Value Functions Day 2 Value Equations Value Equations Value Inequalities
Graphically Algebraically
Holiday

12 13 14 15 16
2.3 Absolute Value
Extra Practice
Review Module 2
TEST
Parent Function: 𝑦 = |𝑥|

Reference Points Graph

Domain: _____________________________

Range: ______________________________

End Behavior: _________________________________________

___________________________________________
Transformation Form 𝑔(𝑥 ) = ±𝑎𝑓|±𝑏(𝑥 − ℎ)| + 𝑘

Examples:

Equation Transformation

𝑔(𝑥) = |𝑥| − 4

𝑔(𝑥) = |𝑥 + 5|

1
𝑔(𝑥) = |𝑥|
4

𝑔(𝑥) = −|3(𝑥 − 1)| + 2

Graph:
1
𝑔(𝑥) = − |𝑥 + 6| + 4
5
Graphing Absolute Value Functions Name: __________________________

Module 2.1, page 73 1 – 13 Date: _____________ Per: _________

a. Predict how the graph of g(x) is a transformation of the graph of f(x) = |x|.

b. Sketch a graph of the function and list the transformations.

7
1. 𝑔(𝑥) = 5|𝑥 − 3| 2. 𝑔(𝑥) = −4|𝑥 + 2| + 5 3. 𝑔(𝑥) = |5 (𝑥 − 6)| + 4

3 7
4. 𝑔(𝑥) = |7 (𝑥 − 4)| + 2 5. 𝑔(𝑥) = 4 |𝑥 − 2| − 3
Graph the given function and identify the domain and range in inequality notation.
4 7
6. 𝑔(𝑥) = |𝑥| 7. 𝑔(𝑥) = |𝑥 − 5| + 7 8. 𝑔(𝑥) = − |𝑥 − 2|
3 6

D: ________________ D: ________________ D: ________________

R: ________________ R: ________________ R: ________________

3 5 7
9. 𝑔(𝑥) = | (𝑥 − 2)| − 7 10. 𝑔(𝑥) = | (𝑥 − 4)| 11. 𝑓(𝑥) = |− (𝑥 + 5)| − 4
4 7 3

D: ________________ D: ________________ D: ________________

R: ________________ R: ________________ R: ________________

Write the absolute value function in the form 𝒈(𝒙) = 𝒂|𝒃(𝒙 − 𝒉)| + 𝒌 for the given graph. Use a or b as directed,
b > 0.

12. Let a = 1 13. Let b = 1

14. List the transformations: 𝑔(𝑥) = −3|2𝑥 + 10| − 4

2.1 Writing Equations of Absolute Value Equations Name ________________________
Notes 2.1 Day 2

Write an equation for each of the graphs.

1. 2. 3.

4. 5. 6.
7. At a science museum exhibit, a beam of light originates from a point on a wall 10 feet off
the floor. It is reflected off a mirror lying on the floor that is 15 feet from the wall from which
the light originates. How high off the floor on the opposite wall does the light hit if the other
wall is 8.5 feet from the mirror?

a) Draw a picture.

b) Write the equation

c) Answer the question

ON YOUR OWN:
8. Two students are passing a ball back and forth, allowing it to bounce once between them. If
one student bounce-passes the ball from a height of 1.4 m and it bounces 3 m away from the
student, where should the second student stand to catch the ball at a height of 1.2 m? Assume
the path of the ball is linear over this short distance.
Name: _____________________________ Date: _________________ Class Period: ______________
Module 2: 2.1 Graphing Absolute Value Functions Day2
Directions:
a. Identify the transformation from the parent function ( y = x ) for each of the following equations.
b. State the domain and range of the equation using interval notation.

1. y = 2 x − 3 2. y = −2 x − 3 + 1

Transformation: Transformation:

Domain: Range: Domain: Range:

1
3. y = x − 5 − 4 4. y = x +3
5

Transformation: Transformation:

Domain: Range: Domain: Range:

1
5. y= x +1 − 2 6. y = − x + 6
3

Transformation: Transformation:

Domain: Range: Domain: Range:

7. y = x − 9 8. y = −3 x − 6

Transformation: Transformation:

Domain: Range: Domain: Range:

Graph the following using transformations.
1. 𝑓(𝑥) = |𝑥 − 5| − 3 2. 𝑓(𝑥) = −|𝑥 + 2| + 1

1
3. 𝑓(𝑥) = 3 |𝑥| − 6 4. 𝑓(𝑥) = − 2 |𝑥 − 5| + 4

Write the equation of an absolute value function that has:

5. shifted down 5 units 6. shifted left 4 units 7. vertex at (-4, -5) with a
vertical stretch by 3

8. vertex at (1, 6) 9. graph 10. graph

Module 2.2 Day 1 Name _________________________________
Solve by graphing

Solve the following absolute value equations by graphing.

1. |x – 3 | + 2 = 5 2. 2| x + 1 | + 5 = 9

3
3. -2|x + 5 | + 4 = 2 4. | 2 (x – 2) | + 3 = 2

Solve each absolute value equation algebraically. Graph the solutions on a number line.

1
5. | 2x | = 3 6. | 3 x + 4 | = 3 7. 3| 2x – 3| + 2 = 3
 1
8. -8 | -x – 6 | + 10 = 2 9. |x+2|+7=5 10. -3| x – 3 | + 3 = 6
4

11. 2(| x + 4 | + 3 ) = 6 12. | 3x - 4 |+ 2 =1 13. |2(x + 5) – 3 | + 2 = 6

14. The bottom of a river makes a V-shaped that can be modeled with the absolute value function,
1
d(h) = 5 | h – 240 | – 48 , where d is the depth of the river bottom ( in feet) and h is the horizontal distance to
the left-handed shore (in feet).

A ship risks running aground if the bottom of its keep (its lowest point under the water) reaches down to the
river bottom. Suppose you are the harbormaster and you want to place buoys where the river bottom is 30
feet below the surface. How far from the left-hand shore should you place the buoys?
Just for fun.

15. An absolute function has a vertex at (5, -4) and contains the points (-1, -7) and (13, -8). Write a possible
equation for the graph.

3 𝑥+9
16. Solve: a) =9 b) 3 – [ 5 – 2(3x – 7)] + 12x = -10
𝑥−7

3𝑥−5
17. Find the inverse of 𝑦 = 7
HAlg 2 Name
2.2 Day 2: Solving Absolute Value Equations

Solve, showing all work.

2c
1. k - 3 = 7 2. 6 - m = -9 3. =3
3

4. k + 19 = 6 5. 6 − 7c = 29 6. ― 2 + 7c = -23

5(2 − 3a)
7. 10 = 8. 64 = 8 5 − x 9. 15 = 9 - 2 2c − 1
6
10. 14 = 8h − 2 + 6 11. 1 − 2z = 4 + z 12. 6 – r = 3r + 1

13. 8b – 9 = 6b − 5 14. 2 + 3t = 6 + 5t

2.2 Solving Absolute Value Equations

1. 2. 3.

4. 5. 6.

7. 8. 9.
10. 11. 12.

13. 14. 15.

16. Is always, sometimes, or never true? Justify your answer.

17. Which statement is equivalent to ?

A. B. C. D.

18. How many solutions does have?

A. ∞ number B. two C. one D. zero

Honors Algebra 2 Name______________________________
2.3 Day 2 Solving Absolute Value Inequalities

Solve Graphically. Highlight your solution and write it in interval notation

1) x − 5 - 3 < 4 2) - x − 5 + 4 < -1

______________________________ ______________________________

Solve algebraically then graph on a number line. Write solutions in interval notation.

d
3. n ≥ 6 4. c ≥ -7 5. ≥6
−5
 x 3
6. --3 k > -33 7. ≥ 8. c - 3 < 4
5 10

2 1
9. g + 3 > 9 10. 15 − 3y ≤ 15 11. c− ≥3
3 2
H Algebra 2: Absolute Value Test Review Name: ____________________________

Describe the transformations to f(x) = |x| for the following. State the domain and range.

1. 𝑔(𝑥) = |𝑥 – 2| + 3 2. 𝑔(𝑥) = −|𝑥| + 7 3. 𝑔(𝑥) = 4|𝑥 + 8| – 6

D: _______ R: _________ D: _______ R: _________ D: _______ R: _________

Solve and graph on a number line.

4. |𝑥 + 3| – 13 = −10 5. −2|𝑥 – 4| = 5

1
6. |2𝑥 − 8| = 3𝑥 − 7 7. 7
|𝑥 + 8| + 3 ≤ 5
8. |𝑥 − 2| − 5 > 10 9. |4 – 𝑥| + 15 > −21

Solve by graphing. Highlight the solution.

−2
10. |𝑥 − 2| + 1 ≤ 5 11. |𝑥 − 3| + 6 = 2 12. −2|𝑥 − 5| + 4 = −4
3

____________________ ____________________ ____________________

 1 1
13. |𝑥 + 3| + 1 > 4 14. − |2 𝑥 + 1| + 1 ≥ -2 15. |𝑥 + 2| + 3 = − 3 𝑥 + 5

____________________ ____________________ ____________________

16. Write the equation 17. Write the equation of f(x) = |x| transformed with a
horizontal stretch of 3 left 4 and down 6.

18. Describe the transformations from f(x) = |x| to

g(x) = 3| -x – 8 | + 5.
____________________