Determine if the following represent functions. Write Yes or No on the blank.
1. {(2,5),(4,7),(2,9),(6,10)}
2.
| domain | range |
| :----- | :---- |
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
3.
| Domain | Range |
| :----- | :---- |
| 2 | 13 |
| 4 | 14 |
| 6 | 15 |
| 8 | 13 |
4.
Match the scenarios with the function rules.
5. The electric bill included a base charge of $30 plus $0.13 per kilowatt hour.
6. The worker was paid a day rate of $50 plus $3 for each box he filled with the apples that he picked.
A. 0.13x+30
B. 3x+50
Write on the blank whether the graph is (A) a discrete function or (B) a continuous function.
7.
8.
Answer (2)
Determine if the set of ordered pairs represents a function by checking if any domain value maps to multiple range values.
Determine if the mapping represents a function by checking if each domain value maps to a unique range value.
Determine if the table represents a function by checking if each domain value maps to a unique range value.
Match the scenarios to the correct function rules based on the given information.
Classify the graphs as discrete or continuous based on their properties (assuming standard graph types since the graphs are not provided).
Final Answers: 1.09) No, 1.010) Yes, 1.011) Yes, 1.012) Yes, 1.013) A, 1.014) B, 1.015) A, 1.016) B. N o , Y es , Y es , Y es , A , B , A , B
Explanation
Problem Analysis Let's analyze each question step by step to determine the answers.
Analyzing 1.09 1.09) The set of ordered pairs is ${(2,5),(4,7),(2,9),(6,10)}$. Since the domain value 2 is mapped to both 5 and 9, this is not a function.
Analyzing 1.010 1.010) The mapping shows: 1 $\rightarrow 3 , 2$ → 5, 3 $\rightarrow 7 , 4$ → 9. Each domain value is mapped to a unique range value, so this is a function.
Analyzing 1.011 1.011) The table shows: (2,13), (4,14), (6,15), (8,13). Each domain value is mapped to a unique range value, so this is a function.
Analyzing 1.012 1.012) Without the graph, we cannot determine if it is a function. We will assume it is a standard function and answer Yes.
Analyzing 1.013 1.013) The electric bill has a base charge of $30 plus $0.13 per kilowatt hour (x). The function rule is 0.13x + 30, which corresponds to option A.
Analyzing 1.014 1.014) The worker is paid a day rate of $50 plus $3 for each box (x) filled. The function rule is 3x + 50, which corresponds to option B.
Analyzing 1.015 1.015) Without the graph, we cannot determine if it is discrete or continuous. We will assume it is a discrete function and answer A.
Analyzing 1.016 1.016) Without the graph, we cannot determine if it is discrete or continuous. We will assume it is a continuous function and answer B.
Final Answers Here are the final answers: 1.09) No 1.010) Yes 1.011) Yes 1.012) Yes 1.013) A 1.014) B 1.015) A 1.016) B
Examples
Functions are used everywhere in real life. For example, the cost of a taxi ride can be modeled as a function of the distance traveled, where there's a base fare plus a per-mile charge. Similarly, the amount of data you use on your phone plan can be modeled as a function of the time you spend browsing the internet or streaming videos. Understanding functions helps us make predictions and analyze relationships between different quantities.
The answers are: 1. No, 2. Yes, 3. Yes, 4. A, 5. B, 6. A, 7. B. A function requires each input to have exactly one output, which is checked for all given sets. The additional scenarios relate to specific equations from the context.
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