Download Algebra 2

Algebra 2
Name:____________________________________
Lesson/Review- Linear Inequalities (graphing and solving)
Date:_____________________________________
Objective:
To review the processes needed for graphing and solving linear inequalities.
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Algebra 2
Lesson- Graphing Absolute Value Functions
Name:____________________________________
Date:_____________________________________
Objective:
To learn how to graph a piecewise and absolute value function
Do Now:
State the domain for f ( x) 
x2 1
x
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Absolute Value Functions
y
Graph the Following
f ( x)  x
x
Now graph each of the following and discuss how each relates to f (x ) from above.
g ( x)  2 x
h( x)  2 x  3
i ( x)  2 x  3
y
y
x
y
x
x
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Algebra 2
Solving Absolute Value Equations
Name:____________________________________
Date:_____________________________________
Objectives: To learn to solve absolute value equations and absolute inequalities.
Absolute Value Equations
ax  b  c
To solve ax  b  c create 2 equations 
and solve each.
ax  b  c
Example:
3x  1  2
Practice:
a. x  1  4
b. 3  y  5
c. 2  3d  4
d . 2m  1  2
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Algebra 2
Lesson- Solving Absolute Value Inequalities
Name:____________________________________
Date:_____________________________________
Objectives: To learn to solve absolute value inequalities.
Absolute Value Inequalities
There are three absolute value situations:
Case 1
ax  b  c
Case 2
ax  b  c
Case 3
ax  b  c
ax  b  c
ax  b  c
 c  ax  b  c
Either ax  b  c or ax  b  c
Examples:
a.
3x  1  2
b.
3x  1  2
c.
3x  1  2
d.
3x  1  2
Practice:
a. x  1  4
b. 3  y  5
c. 2  3d  4
d . 2m  1  2
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Algebra 2
Name:____________________________________
WKST- Mixed equation/inequality and absolute value set
Date:_____________________________________
Answer each of the following neatly and completely in the space provided.
Solve and graph each inequality:
1.
x  7x  6
2.
x  3  3(2 x  1)
3.
x3  4
4.
2x  5  x  1
5.
2x  3  5
6.
2 x  8
7.
x 2  2 x  24  0
8.
x 2  10 x  1  0
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9.
x2  4  0
10.
x2  8x  7  0
11.
3x 2  10 x  8
12.
5d  7  28
13. Explain why the solution set of
x 2  9  0 is all real numbers.
14. Explain why the solution set of
x 2  16  0 is empty.
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Algebra 2
Lesson- Graphing Piecewise Functions
Name:____________________________________
Date:_____________________________________
Objective:
To learn how to graph piecewise functions.
Do Now: Graph: f ( x)  3x  2 for  3  x  0
y
x
What is a piecewise function?
Graph the following:
2 x if x  0
f ( x)  
2 if x  0
y
x
2 x  1 if x  0
g ( x)   2
 x if x  0
y
x
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Algebra 2
Name:__________________________________
Mixed Wkst: Graphing Absolute and Piecewise Functions
Date:___________________________________
y
1. Graph the following function:
x  2 if x  1
f ( x)  
x  2 if x  1
x
2. Graph each function, and state the domain and range
(1)
f ( x)  x  3
(2)
f ( x)  3 x  2
y
y
x
x
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Algebra 2
Lesson- Direct and Inverse Variation
Name:____________________________________
Date:_____________________________________
Objective:
To learn how to distinguish between direct and inverse variation (and use both).
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ANSWER KEYS
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