Type The Correct Answer In Each Box.Consider The Table Modeling A Function:${ \begin{tabular}{|c|c|c|c|c|c|} \hline X X X & -2 & -1 & 0 & 1 & 2 \ \hline F ( X ) F(x) F ( X ) & -28 & -9 & -2 & -1 & 0 \ \hline \end{tabular} }$Complete The Table Modeling The
Type the correct answer in each box. Consider the table modeling a function:
Understanding the Table Modeling a Function
When we encounter a table modeling a function, it's essential to understand the relationship between the input values (x) and the corresponding output values (f(x)). In this case, we have a table with five input values (-2, -1, 0, 1, and 2) and their corresponding output values (-28, -9, -2, -1, and 0).
The Table Modeling a Function
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| f(x) | -28 | -9 | -2 | -1 | 0 |
Identifying the Pattern
To complete the table, we need to identify the pattern or relationship between the input values and the output values. Let's examine the differences between consecutive output values:
- From x = -2 to x = -1, the difference in f(x) is -28 - (-9) = -19.
- From x = -1 to x = 0, the difference in f(x) is -9 - (-2) = -7.
- From x = 0 to x = 1, the difference in f(x) is -2 - (-1) = -1.
- From x = 1 to x = 2, the difference in f(x) is -1 - 0 = -1.
We can observe that the differences between consecutive output values are decreasing by 2, 6, and 0, respectively. This suggests that the function is decreasing at a decreasing rate.
Determining the Next Output Value
To determine the next output value, we need to find the difference between the current output value and the next input value. Since the differences are decreasing by 2, 6, and 0, we can expect the next difference to be -3 (decreasing by 3 from the previous difference of -1).
The next input value is x = 3, and the previous output value is f(2) = 0. Therefore, the next output value is f(3) = 0 - 3 = -3.
Completing the Table
Now that we have determined the next output value, we can complete the table:
| x | -2 | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|
| f(x) | -28 | -9 | -2 | -1 | 0 | -3 |
Conclusion
In conclusion, we have completed the table modeling the function by identifying the pattern or relationship between the input values and the output values. We determined the next output value by finding the difference between the current output value and the next input value, and we completed the table accordingly.
Key Takeaways
- When given a table modeling a function, it's essential to understand the relationship between the input values and the output values.
- Identifying the pattern or relationship between the input values and the output values is crucial in completing the table.
- Determining the next output value involves finding the difference between the current output value and the next input value.
Final Answer
The completed table modeling the function is:
| x | -2 | -1 | 0 | 1 | 2 | 3 | |
|---|---|---|---|---|---|---|---|
| f(x) | -28 | -9 | -2 | -1 | 0 | -3 |
Type the correct answer in each box. Consider the table modeling a function: Q&A
Understanding the Table Modeling a Function
When we encounter a table modeling a function, it's essential to understand the relationship between the input values (x) and the corresponding output values (f(x)). In this case, we have a table with five input values (-2, -1, 0, 1, and 2) and their corresponding output values (-28, -9, -2, -1, and 0).
The Table Modeling a Function
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| f(x) | -28 | -9 | -2 | -1 | 0 |
Q&A Session
Q: What is the relationship between the input values and the output values in the table?
A: The relationship between the input values and the output values in the table is a function. The function takes the input values (x) and produces the corresponding output values (f(x)).
Q: How do we identify the pattern or relationship between the input values and the output values?
A: We can identify the pattern or relationship between the input values and the output values by examining the differences between consecutive output values. In this case, the differences are decreasing by 2, 6, and 0, respectively.
Q: How do we determine the next output value?
A: To determine the next output value, we need to find the difference between the current output value and the next input value. Since the differences are decreasing by 2, 6, and 0, we can expect the next difference to be -3 (decreasing by 3 from the previous difference of -1).
Q: What is the next output value?
A: The next output value is f(3) = 0 - 3 = -3.
Q: How do we complete the table?
A: We complete the table by adding the next input value (x = 3) and the corresponding output value (f(3) = -3).
Q: What is the completed table?
A: The completed table is:
| x | -2 | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|
| f(x) | -28 | -9 | -2 | -1 | 0 | -3 |
Key Takeaways
- When given a table modeling a function, it's essential to understand the relationship between the input values and the output values.
- Identifying the pattern or relationship between the input values and the output values is crucial in completing the table.
- Determining the next output value involves finding the difference between the current output value and the next input value.
Final Answer
The completed table modeling the function is:
| x | -2 | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|
| f(x) | -28 | -9 | -2 | -1 | 0 | -3 |
Additional Questions and Answers
Q: What if the differences between consecutive output values are not decreasing?
A: If the differences between consecutive output values are not decreasing, we may need to re-examine the table and look for a different pattern or relationship.
Q: How do we handle negative input values?
A: When handling negative input values, we need to be careful to ensure that the function is defined for those values. In this case, the function is defined for all input values, including negative values.
Q: Can we use this table to make predictions about the function?
A: Yes, we can use this table to make predictions about the function. By examining the pattern or relationship between the input values and the output values, we can make educated guesses about the function's behavior for other input values.
Conclusion
In conclusion, we have completed the table modeling the function by identifying the pattern or relationship between the input values and the output values. We determined the next output value by finding the difference between the current output value and the next input value, and we completed the table accordingly.