Precalculus Test 1 Review: Step-by-Step Guidance

스터디 가이드 - 스마트 노트

자료에 맞춘 맞춤형 노트, 핵심 정의, 예시, 맥락을 확장해 제공합니다.

Q1. Is the relation {(9, 0), (0, 9), (8, 3), (4, 9), (3, 0), (9, 3), (2, 0)} a function? State its domain and range.

Background

Topic: Relations and Functions

This question tests your understanding of the definition of a function, as well as how to determine the domain and range from a set of ordered pairs.

Key Terms and Concepts:

Function: A relation where each input (x-value) is paired with exactly one output (y-value).
Domain: The set of all possible input values (x-values).
Range: The set of all possible output values (y-values).

Step-by-Step Guidance

List all the x-values from the given set. These will help you determine the domain.
Check if any x-value is repeated with a different y-value. If so, the relation is not a function.
List all the y-values to determine the range.
Write the domain and range as sets.

Try solving on your own before revealing the answer!

Final Answer:

The relation is not a function because the input 9 is paired with both 0 and 3.

Domain: {2, 3, 4, 8, 9, 0}

Range: {0, 3, 9}

Since 9 appears as an x-value more than once with different y-values, the relation fails the definition of a function.

Q2. Is the relation {(-2, 0), (0, -5), (-5, 6), (-6, 3), (1, 2)} a function? State its domain and range.

Background

Topic: Relations and Functions

This question is similar to the previous one, focusing on identifying functions and determining domain and range from a set of ordered pairs.

Key Terms and Concepts:

Function: Each x-value must correspond to only one y-value.
Domain: All x-values in the set.
Range: All y-values in the set.

Step-by-Step Guidance

List all x-values and check for repeats with different y-values.
If no x-value is repeated, the relation is a function.
List all y-values for the range.
Write the domain and range as sets.

Try solving on your own before revealing the answer!

Final Answer:

The relation is a function because each x-value is unique.

Domain: {-6, -5, -2, 0, 1}

Range: {0, -5, 2, 3, 6}

Each input is paired with exactly one output, so this is a function.

Q3. For the relation represented by the following table, is it a function? State the domain and range.

-5	-4	-3	-2	-1	1	2	3	4	5
1	2	3	4	5	-5	-4	-3	-2	-1

Background

Topic: Relations and Functions

This question asks you to interpret a table of values as a relation and determine if it is a function, as well as to find the domain and range.

Key Terms and Concepts:

Function: Each x-value must correspond to only one y-value.
Domain: All x-values in the table.
Range: All y-values in the table.

Step-by-Step Guidance

Check if any x-value appears more than once with different y-values.
If each x-value is paired with only one y-value, it is a function.
List all x-values for the domain and all y-values for the range.

Try solving on your own before revealing the answer!

Final Answer:

This relation is a function because each x-value is paired with only one y-value.

Domain: {-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}

Range: {1, 2, 3, 4, 5, -5, -4, -3, -2, -1}

Q4. For the relation represented by the following table, is it a function? State the domain and range.

-5	-4	-3	-2	-1	1	2	3	4	5
1	2	3	4	5	-5	-4	-3	-2	-1

Background

Topic: Relations and Functions

This is a repeat of the previous question, likely to reinforce the concept.

Key Terms and Concepts:

Function: Each x-value must correspond to only one y-value.
Domain: All x-values in the table.
Range: All y-values in the table.

Step-by-Step Guidance

Check for repeated x-values with different y-values.
If each x-value is unique, the relation is a function.
List the domain and range.

Try solving on your own before revealing the answer!

Final Answer:

This relation is a function for the same reasons as above.

Domain: {-5, -4, -3, -2, -1, 1, 2, 3, 4, 5}

Range: {1, 2, 3, 4, 5, -5, -4, -3, -2, -1}