The Table Below Represents A Function.${ \begin{tabular}{|l|c|c|c|c|c|} \hline X X X & 1 & 2 & 3 & 4 & 5 \ \hline Y Y Y & 6 & 12 & 18 & 24 & 30 \ \hline \end{tabular} }$Which Statement Would Best Describe The Graph Of The Function?A. The Graph
Introduction
In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. The table below represents a function, where each input value of is associated with a unique output value of . In this article, we will explore the characteristics of the graph of this function and determine which statement best describes it.
The Table
| 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|
| 6 | 12 | 18 | 24 | 30 |
Understanding the Graph
The graph of a function is a visual representation of the relationship between the input values and the output values. In this case, the graph will be a straight line, as the output values increase by a constant amount for each increase in the input values.
Characteristics of the Graph
The graph of the function has several characteristics that can be determined from the table:
- Increasing trend: The output values increase by a constant amount for each increase in the input values, indicating an increasing trend.
- Linear relationship: The graph is a straight line, indicating a linear relationship between the input values and the output values.
- Positive slope: The graph has a positive slope, indicating that the output values increase as the input values increase.
Statement Options
Based on the characteristics of the graph, we can evaluate the statement options:
- A. The graph is a straight line with a positive slope: This statement accurately describes the graph of the function.
- B. The graph is a curve with a negative slope: This statement is incorrect, as the graph is a straight line with a positive slope.
- C. The graph is a horizontal line: This statement is incorrect, as the graph is a straight line with a positive slope.
- D. The graph is a vertical line: This statement is incorrect, as the graph is a straight line with a positive slope.
Conclusion
In conclusion, the graph of the function represented by the table is a straight line with a positive slope. This can be determined by analyzing the characteristics of the graph, including the increasing trend, linear relationship, and positive slope.
Key Takeaways
- The graph of a function is a visual representation of the relationship between the input values and the output values.
- The graph of the function represented by the table is a straight line with a positive slope.
- The characteristics of the graph, including the increasing trend, linear relationship, and positive slope, can be determined from the table.
Further Exploration
Introduction
In our previous article, we explored the characteristics of the graph of a function represented by a table. In this article, we will answer some frequently asked questions about the table and its graph.
Q&A
Q: What is the domain of the function represented by the table?
A: The domain of the function is the set of input values, which in this case is {1, 2, 3, 4, 5}.
Q: What is the range of the function represented by the table?
A: The range of the function is the set of output values, which in this case is {6, 12, 18, 24, 30}.
Q: Is the function represented by the table a linear function?
A: Yes, the function represented by the table is a linear function, as the output values increase by a constant amount for each increase in the input values.
Q: What is the slope of the graph of the function represented by the table?
A: The slope of the graph of the function represented by the table is 6, as each increase in the input values results in an increase of 6 in the output values.
Q: Is the graph of the function represented by the table a straight line?
A: Yes, the graph of the function represented by the table is a straight line, as the output values increase by a constant amount for each increase in the input values.
Q: Can the graph of the function represented by the table be described as increasing, decreasing, or constant?
A: The graph of the function represented by the table can be described as increasing, as the output values increase by a constant amount for each increase in the input values.
Q: Can the function represented by the table be described as a one-to-one function?
A: Yes, the function represented by the table can be described as a one-to-one function, as each input value is associated with a unique output value.
Q: Can the function represented by the table be described as an onto function?
A: Yes, the function represented by the table can be described as an onto function, as each output value is associated with at least one input value.
Q: Can the function represented by the table be described as a bijection?
A: Yes, the function represented by the table can be described as a bijection, as it is both one-to-one and onto.
Conclusion
In conclusion, the table represents a function with a linear graph that is increasing, one-to-one, onto, and a bijection. We hope that this Q&A article has provided you with a better understanding of the characteristics of the graph of the function represented by the table.
Key Takeaways
- The domain of the function represented by the table is {1, 2, 3, 4, 5}.
- The range of the function represented by the table is {6, 12, 18, 24, 30}.
- The function represented by the table is a linear function.
- The slope of the graph of the function represented by the table is 6.
- The graph of the function represented by the table is a straight line.
- The graph of the function represented by the table is increasing.
- The function represented by the table is one-to-one.
- The function represented by the table is onto.
- The function represented by the table is a bijection.
Further Exploration
For further exploration, you can try creating a graph of the function using a graphing tool or software. You can also try modifying the table to create a new function and analyzing its graph.