Unit 6 Alg 1
Name:_________________________
Period:______
Unit 6 Note Packet
List of topics for this unit/Assignment tracker
Topic
Assignment & Due Date
Date
Graphing Absolute Value Equations Part 1
Graphing Absolute Value Equations Part 2
OC 6.2 Translating the Graph of 𝑓 𝑥 = 𝑥
Quiz 1
OC 6.3 Stretching, Shrinking, and Reflecting the Graph
of 𝑓 𝑥 = 𝑥
OC 6.4 Combining Transformations of the Graph of
𝑓 𝑥 = 𝑥
Quiz 2
6.5 Solve Absolute Value Equations
OC 6.5 Solving Absolute Value Equations
Quiz 3
Review
Test
This packet is due for 100 points on the day of the test. 10 points will be deducted for each section of
notes that is missing. 5 points will be deducted for each warm up that is missing. If you’re absent,
get the notes and warm up from me or a classmate.
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Unit 6 Alg 1
Graphing Absolute Value Equations Part 1
Date:
WARM UP
Graph each.
𝟏
1. 𝒚 = 𝟑 𝒙 − 𝟐
3. 𝒙 = 𝟑
2. 𝟐𝒙 + 𝟑𝒚 = 𝟔
Review Vocabulary
Absolute Value
Guided Practice
Simplify.
1. −10
2. 12 − 19
3. 20 − 8
Your Turn
4. 4.5
5. 9 ∙ −5
6. − 17
Guided Practice
7. Graph 𝑦 = 𝑥
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8. Graph 𝑦 = 3𝑥
Your Turn
9. Graph 𝑦 =
1
2
𝑥
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Guided Practice
10. Graph 𝑦 = 𝑥 − 5
Your Turn
11. Graph 𝑦 = 𝑥 + 4
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𝟏. 𝒚 = 𝟒𝒙
𝟒. 𝒚 = 𝒙 − 𝟔
Graphing Absolute Value Equations Part 1 Assignment
2. 𝒚 = −𝒙
𝟑. 𝒚 = −𝟑𝒙
5. 𝒚 = 𝒙 + 𝟐
𝟔. 𝒚 = 𝒙 − 𝟑
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Graphing Absolute Value Equations Part 2
WARM UP
Graph each.
1. y = x + 1
Date:
2. 𝑦 = 2𝑥
Graphing Absolute Value Functions
𝒚=𝒂 𝒙−𝒉 +𝒌
How a changes the graph:
How h changes the graph:
How k changes the graph:
Guided Practice
1. Graph 𝑦 = − 𝑥 + 2 + 3
x
y
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2. Graph 𝑦 = 2 𝑥 + 6 − 5
Your Turn
3. Graph 𝑦 = − 𝑥 + 3 − 4
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Guided Practice
Write an equation of the graph.
4.
5.
Your Turn
6.
7.
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𝟏. 𝒚 = 𝟔 𝒙 − 𝟕
Graphing Absolute Value Equations Part 2 Assignment
2. 𝒚 = 𝒙 + 𝟗
𝟑. 𝒚 = − 𝒙 − 𝟖 + 𝟏
𝟒. 𝒚 = − 𝒙 + 𝟐 + 𝟏𝟏
5. 𝒚 = 𝟐 𝒙 + 𝟐 + 𝟑
𝟔. 𝒚 = 𝟑 𝒙 − 𝟏 − 𝟑
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OC 6.2 Translating the Graph of 𝒇 𝒙 = 𝒙
WARM UP
Graph each.
1. y = x + 1
Date:
2. y = x − 1 − 3
1 ENGAGE Understanding the Parent Absolute Value Function
The most basic absolute value function is a given by the following rule.
f(x) = |x|
This function is sometimes called the parent absolute
value function.
To graph the function, you can make a table of values
like the one shown, plot the ordered pairs, and draw
the graph.
As shown at the right, the function's V-shaped graph
consists of two rays with a common endpoint at (0, 0). This point is
called the vertex of the graph.
REFLECT
1a. What is the domain of f(x) = |x|? What is the range?
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1b. If you fold the graph of f(x) = |x| over the y-axis, the two halves of the graph match up perfectly. The graph
is said to be symmetric about the y-axis. Explain why it makes sense that the graph of f(x) = |x| is symmetric
about the y-axis.
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1b. For what values of x is the function f(x) = |x| increasing? decreasing?
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2 EXAMPLE Graphing Functions of the Form g(x) = |x − h| + k
Graph each absolute value function. (The graph of the parent function f(x) = |x| is shown in gray.)
A g(x) = |x| + 2
B g(x) = |x − 4|
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C g(x) = |x − 4| + 2
REFLECT
2a. How is the graph of g (x) = |x| + 2 related to the graph of the parent function f(x) = |x|?
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2b. How do you think the graph of g(x) = |x| − 2 would be related to the graph of the parent function f(x) =
|x|?
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2c. How is the graph of g(x) = |x − 4| related to the graph of the parent function f(x) = |x|?
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2d. How do you think the graph of g(x) = |x + 4| would be related to the graph of the parent function f(x) =
|x|?
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2e. How is the graph of g(x) = |x − 4| + 2 related to the graph of the parent function f(x) = |x|?
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2f. Predict how the graph of g(x) = |x + 3| − 5 is related to the graph of the parent function f(x) = |x|. Then
check your prediction by making a table of values and graphing the function. (The graph of f(x) = |x| is
shown in gray.)
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2g. In general, how is the graph of g(x) = |x − h| + k related to the graph of f(x) = |x|?
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EXAMPLE Writing Equations for Absolute Value
Functions
Write the equation for the absolute value function whose graph is
shown.
A Compare the given graph to the graph of the parent function f(x) = |x|.
Complete the table to describe how the parent function must be translated
to get the graph shown here.
B Determine the values of h and k for the function g(x) = |x − h| + k.
•h is the number of units that the parent function is translated horizontally. For a translation to the
right, h is positive; for a translation to the left, h is negative.
•k is the number of units that the parent function is translated vertically. For a translation up, k is
positive; for a translation down, k is negative.
So, h =
and k =
. The function is
.
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REFLECT
3a. What can you do to check that your equation is correct?
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3b. If the graph of an absolute value function is a translation of the graph of the parent function, explain
how you can use the vertex of the translated graph to help you determine the equation for the function.
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3c. Suppose the graph in the Example is shifted left one unit so that the vertex is at (1, 3). What will be the
equation of that absolute value function?
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OC 6.2 Translating the Graph of 𝒇 𝒙 = 𝒙 Assignment
Graph each absolute value function.
Write the equation of each absolute value function whose graph is shown.
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OC 6.3 Stretching, Shrinking, and Reflecting the Graph of 𝒇 𝒙 = 𝒙
Date:
WARM UP
Graph each.
1. y = x + 2 − 5
2. y = x − 3 + 1
1 EXAMPLE Graphing g(x) = a|x| when |a| > 1
Graph each absolute value function using the same coordinate plane. (The graph of the parent
function f(x) = |x| is shown in gray.)
A g(x) = 2|x|
B g(x) = –2|x|
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Unit 6 Alg 1
REFLECT
1a. The graph of the parent function f(x) = |x| includes the point (–1, 1) because f(−1) = |–1| = 1. The
corresponding point on the graph of g(x) = 2|x| is (–1, 2) because g(–1) = 2|–1| = 2. In general, how does the
y-coordinate of a point on the graph of g(x) = 2|x| compare with the y-coordinate of a point on the graph of
f(x) = |x| when the points have the same x-coordinate?
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1b. Describe how the graph of g(x) = 2|x| compares with the graph of f(x) = |x|. Use either the word stretch
or shrink, and include the direction of the movement.
1c.What other transformation occurs when the value of a in g(x) = a|x| is negative?
2 EXAMPLE Graphing g(x) = a|x| when |a| < 1
Graph each absolute value function using the same coordinate plane. (The graph of the parent
function f(x) = |x| is shown in gray.)
REFLECT
1
2a. How does the y-coordinate of a point on the graph of 𝑔 𝑥 = 4 𝑥 compare with the y-coordinate of a
point on the graph of f(x) = |x| when the points have the same x-coordinate?
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1
2b. Describe how the graph of 𝑔(𝑥) = 4 𝑥 compares with the graph of f(x) = |x|. Use either the word stretch
or shrink, and include the direction of the movement.
2c.What other transformation occurs when the value of a in g(x) = a|x| is negative?
2d. Compare the domain and range of g(x) = a|x| when a> 0 and when a< 0.
2e. Summarize your observations about the graph of g(x) = a|x|
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Unit 6 Alg 1
OC 6.3 Stretching, Shrinking, and Reflecting the Graph of 𝒇 𝒙 = 𝒙 Assignment
Graph each absolute value function.
Write the equation of each absolute value function whose graph is shown.
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OC 6.4 Combining Transformations of the Graph of 𝒇 𝒙 = 𝒙
Date:
WARM UP
Graph each.
1. y = 2 x − 1 − 2
1
2.y = − 2 x + 2 + 4
EXAMPLE Graphing g(x) = a|x− h| and g(x) = a|x| + k
Graph each absolute value function. (The graph of the parent function f(x) = |x| is shown in gray.)
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REFLECT
1
1a. How is the graph of 𝑔(𝑥) = 2 |𝑥 − 3| related to the graph of f(x) = |x|?
1b. How is the graph of g(x) = 3|x| − 7 related to the graph of f(x) = |x|?
1
1
1
1c. How is the graph of 𝑔(𝑥) = 2 |𝑥 − 3| affected if you replace 2 with − 2 and 3 with −3?
2 EXAMPLE Graphing g(x) = a|x − h| + k
Graph g(x) = −2|x + 1| + 3. (The graph of the parent
function f(x) = |x| is shown in gray.)
REFLECT
2a. How is the graph of g(x) = − 2|x + 1| + 3 related to the
graph of f(x) = |x|?
2b. How is the graph of g(x) = −2|x + 1| + 3 affected if you
replace 3 with −3?
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2c. Complete the table to summarize how you can obtain the graph of g(x) = a|x − h| + k from the graph of
the parent function f(x) = |x|.
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OC 6.4 Combining Transformations of the Graph of 𝒇 𝒙 = 𝒙 Assignment
Graph each absolute value function.
Write the equation for each absolute value function whose graph is shown.
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6.5 Solve Absolute Value Equations
WARM UP
Graph each.
1. y = −2 x
Date:
1
2. y = − 2 x
Vocabulary
Absolute Value Equation
Guided Practice
1. Solve 𝑥 = 7
Your Turn
Solve
2. 𝑥 = −3
3. 𝑥 = 15
Solving an Absolute Value Equation
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Unit 6 Alg 1
Guided Practice
4. 𝑥 − 3 = 8
5.
4𝑥 − 5 = 18
Your Turn
6. 𝑟 − 7 = 9
7. 2𝑥 + 7 = 11
Guided Practice
8. 3 2𝑥 − 7 − 5 = 4
Your Turn
9. 2 𝑠 + 4.1 = 18.9
10. 4 𝑡 + 9 − 5 = 19
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Guided Practice
11. Solve 3𝑥 + 5 + 6 = −2 , if possible.
Your Turn
Solve the equation, if possible.
12. 2 𝑚 − 5 + 4 = 2
13. −3 𝑛 + 2 − 7 = −10
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6.5 Solve Absolute Value Equations Assignment
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OC 6.5 Solving Absolute Value Equations
Date:
WARM UP
1.
2.
1 EXAMPLE Solving an Absolute Value Equation by Graphing
Solve the equation 2|x − 3| + 1 = 5 by graphing.
A Treat the left side of the equation as the absolute value function f(x) = 2|x − 3| + 1. Graph the function by
following these steps.
• Identify and plot the vertex:
• If you move 1 unit to the left or right of the vertex, describe how must
you move vertically to get to a point on the graph. Give the coordinates of
these points and then plot them.
• Use the three plotted points to draw the complete graph.
B Treat the right side of the equation as the constant function g(x) = 5.
Draw the graph of g(x) on the same coordinate plane as the graph of f(x).
C Identify the x-coordinate of each point where the graphs of f(x) and g(x) intersect. Show that each xcoordinate is a solution of 2|x − 3| + 1 = 5.
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B Interpret the equation |x − 3| = 2: What numbers have an absolute value equal to 2?
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OC 6.5 Solving Absolute Value Equations Assignment
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Unit 6 Review
Date:
WARM UP
Solve. 1.
Examples
Evaluate each:
1. −6 + 1
2.
2. − −8 − 4 + 2
3. −2 −8 + 2 − 1
Graph by making a t-table.
4. 𝑦 = 𝑥 + 1 − 3
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Unit 6 Alg 1
Graph by using the translation and transformation methods.
2
5. 𝑦 = 𝑥 − 2 − 4
6. 𝑦 = 3 𝑥 − 5
7. 𝑦 = −3 𝑥 + 2 + 4
Solve each equation.
8.
9.
10.
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Unit 6 Review Assignment
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