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Unit 1 Study Guide (Due 10/31/25)

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Last updated about 2 hours ago
35 questions

This is the study guide for the Unit 1 test.

You will be allowed to use this on the test along with any other assignments and notes.

Complete the entire document for full credit.

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Main Idea: Absolute Value

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Question 16
16.

The definition of absolute value is...

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2
Question 17
17.

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2

Main Idea: Solving Absolute Value Equations

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10
Question 19
19.
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Day 2 10/31/25

Main Idea: Compound Inequalities

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10
Question 24
24.
Solve and graph the compound inequality for the given variable.


_______
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10
Question 25
25.

Main Idea: Solving Absolute Value Inequalities

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Question 26
26.

Solve and graph the inequality

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20

Main Idea: Graphing Absolute Value Functions

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Question 30
30.
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Question 31
31.
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Main Idea: Absolute Value Applications

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Question 35
35.
The number of boats B a boat dealer sells in each month of the year from March to December can be modeled by the function 𝐵 = −15|𝑡 − 5| +120 where t is the time in months and t = 1 represents January.

1)Complete the table of values and then graph the function.

2) What is the maximum number of sales in one month?
_______


3) In what month is the maximum reached?
_______


4) What is the minimum number of sales in one month?
_______

5) In what month is the minimum reached?
_______

Main Idea: Characteristics of Functions






Question 1
1.

Put the interval notations and graphs in the right category.

  • Both
Question 2
2.
Describe the domain of this function.

In interval notation:
_______

As an inequality:
_______

Use these symbols if you can not find them ≥ ≤ ∞
Question 3
3.
Describe the range of this function.

In interval notation:
_______

As an inequality:
_______

Use these symbols if you can not find them ≥ ≤ ∞
Question 4
4.
Describe the domain of this function.

In interval notation:
_______

As an inequality:
_______

Use these symbols if you can not find them ≥ ≤ ∞
Question 5
5.
Describe the range of this function.

In interval notation:
_______

As an inequality:
_______

Use these symbols if you can not find them ≥ ≤ ∞
Question 6
6.
What intervals of x is the function f(x) increasing?

_______ U _______
Question 7
7.

For what interval of x is the function f(x) decreasing?

Question 8
8.

For what interval of x is the function f(x) negative?

Question 9
9.

Name an interval of x is the function f(x) positive?

Question 10
10.

Write the following in interval notation. Use the little side keyboard to find infinity if you need it and type your answer.

Question 11
11.

Write the following in interval notation.

Question 12
12.

What is the domain of the function?

Question 13
13.

What is the range of the function?

Question 14
14.

Use the graph to create a function with the following features:

1) As x gets smaller; the function approaches negative infinity. x→ - ∞; f(x)→ -∞
2) As x gets larger; the function approaches negative infinity. x→ ∞; f(x)→ -∞
3) The graph of the function passes through the x-axis at -2.
4) The graph of the function passes though the y-axis at y=4

Question 15
15.

Vocabulary Review: Mark each statement as True or False.

  • False
  • True
  • The answer to the absolute value of 8 is -8.
  • The absolute value of -8 is -8, since -8 is 8 units from 0 on the number line.
  • The absolute value of -8 is 8, since -8 is 8 units from 0 on the number line.
  • According to the definition of absolute value, if |r|= 3, then r = 3 or r = -3.
Find the absolute value of this expression:
Question 18
18.

Find the absolute value of this expression:

Solve this absolute Value equation:

|-2x+5|= 7

+ Case
_______
- Case
_______
Question 20
20.
Solve this absolute Value equation:

|3x+6|=15

+ Case
_______
- Case
_______
Question 21
21.
Solve this absolute Value equation:

2|4x+6|=36

+ Case
_______
- Case
_______
Question 22
22.
Solve this absolute Value equation:

+ Case
_______
- Case
_______
Question 23
23.
Solve this absolute Value equation:
4|n - 2| – 3 = 25
+ Case
_______
- Case
_______
Solve and graph the compound inequality for the given variable.



_______ or _______
Question 27
27.
Solve and graph the inequality:
+ case
_______
- case
_______
Question 28
28.
Solve and graph the inequality:


+ case
_______
- case
_______
Question 29
29.
Solve and graph.


+ case
_______
- case
_______
How is the absolute function below different than the parent function y=|x|:

y=-4|x-3|+2


Opens (Upward or Downward) _______

Horizontal Shift (write none if there is none) _______

Vertical Shift (write none if there is none) _______

Stretched (0<|a|<1), Compressed (|a|>1), or None
_______
How is the absolute function below different than the parent function y=|x|:





Opens (Upward or Downward) _______

Horizontal Shift (write none if there is none) _______

Vertical Shift (write none if there is none) _______

Stretched (0<|a|<1), Compressed (|a|>1), or None _______.
Question 32
32.
1) What are the critical values of this absolute value function:

y=|x-3|+4

Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______
Slope
_______

2) Use the critical values of this equation to graph it.
Question 33
33.
What are the critical values of this absolute value function:

y=2|x+4|- 2

Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______
Slope
_______

2) Use the critical values of this equation to graph it.
Question 34
34.
What are the critical values of this absolute value function:




Opens (upward or downward)
_______
Axis of Symmetry
_______
Vertex
_______
Slope
_______

2) Use the critical values of this equation to graph it.
(3,5]
[5,∞)
(3,5)
[3,5)
(-∞,-9)
[3.5]
Open Interval
Closed Interval