Question
Complete the tables to show the parent function y=f(x)
and its translation y=f(x+5)
. (2 points)
Original Function
x
y=f(x)
−2
5
−1
2
0 1
1 2
2 5
Translated Function
x
y=f(x+5)
5
2
1
2
5
Remaining Attempts : 3
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and its translation y=f(x+5)
. (2 points)
Original Function
x
y=f(x)
−2
5
−1
2
0 1
1 2
2 5
Translated Function
x
y=f(x+5)
5
2
1
2
5
Remaining Attempts : 3
Skip to navigation
Answers
GPT-4o mini
To find the translated function \( y = f(x + 5) \), we need to realize that the translation involves shifting the function horizontally to the left by 5 units. This means that for each \( x \) in the translated function, the corresponding \( y \) value will be from the original function at \( x + 5 \).
### Original Function
| x | \( y = f(x) \) |
|------|----------------|
| -2 | 5 |
| -1 | 2 |
| 0 | 1 |
| 1 | 2 |
| 2 | 5 |
### Translated Function
To find \( y = f(x + 5) \):
- For \( x = 5 \): Find \( f(5) \) (from original function), but 5 is not in the original x values.
- For \( x = 2 \): Find \( f(2 - 5) = f(-3) \), but -3 is not in the original x values.
- For \( x = 1 \): Find \( f(1 - 5) = f(-4) \), but -4 is not in the original x values.
- For \( x = 0 \): Find \( f(0 - 5) = f(-5) \), but -5 is not in the original x values.
- For \( x = -1 \): Find \( f(-1 - 5) = f(-6) \), but -6 is not in the original x values.
- For \( x = -2 \): Find \( f(-2 - 5) = f(-7) \), but -7 is not in the original x values.
None of the derived x values from the function \( f(x + 5) \) correspond to the provided \( f(x) \).
### Assuming Extension of Original Data
If we extend our understanding:
- For x values included (to figure out the missing values), we can assume some functional forms that might result in values.
However, the specific values for the function \( f(x + 5) \) cannot be produced from the original data provided without additional data for larger inputs, as we cannot find values for \( f(x + 5) \) systematically.
If you require purely the table falling from original data to translated values:
From the original \( f(x) \) table:
- x: -2 gives y=5; for \( f(-2+5) = f(3) \) - need functional information for \( f(3) \) if available.
Since the above original values do not yield specific values derived for \( f(x+5) \) without more data on x.
If we assume that \( f(x) = ax^2 + bx + c \) or some other function-type you may have a different outcome if \( f(3), f(4), ..., f(5) \) data were available.
Thus, above produces no further workings since mapping doesn't correspond; you would need to specify or adjust the function to derive the whole translated table under a composed new set.
To fill in values for x = 5, 2, 1, 0, -1 with some actual functional data for y = f(x + 5), hence the missing functional correlation links need clarify.
To summarize:
- The original table shown has specified points, so deducing from it, we need way to form a valid response - if that helps lead-out any translation that applies.
If more data can amplify that outcome - kindly display shared or specify what's available.
### Original Function
| x | \( y = f(x) \) |
|------|----------------|
| -2 | 5 |
| -1 | 2 |
| 0 | 1 |
| 1 | 2 |
| 2 | 5 |
### Translated Function
To find \( y = f(x + 5) \):
- For \( x = 5 \): Find \( f(5) \) (from original function), but 5 is not in the original x values.
- For \( x = 2 \): Find \( f(2 - 5) = f(-3) \), but -3 is not in the original x values.
- For \( x = 1 \): Find \( f(1 - 5) = f(-4) \), but -4 is not in the original x values.
- For \( x = 0 \): Find \( f(0 - 5) = f(-5) \), but -5 is not in the original x values.
- For \( x = -1 \): Find \( f(-1 - 5) = f(-6) \), but -6 is not in the original x values.
- For \( x = -2 \): Find \( f(-2 - 5) = f(-7) \), but -7 is not in the original x values.
None of the derived x values from the function \( f(x + 5) \) correspond to the provided \( f(x) \).
### Assuming Extension of Original Data
If we extend our understanding:
- For x values included (to figure out the missing values), we can assume some functional forms that might result in values.
However, the specific values for the function \( f(x + 5) \) cannot be produced from the original data provided without additional data for larger inputs, as we cannot find values for \( f(x + 5) \) systematically.
If you require purely the table falling from original data to translated values:
From the original \( f(x) \) table:
- x: -2 gives y=5; for \( f(-2+5) = f(3) \) - need functional information for \( f(3) \) if available.
Since the above original values do not yield specific values derived for \( f(x+5) \) without more data on x.
If we assume that \( f(x) = ax^2 + bx + c \) or some other function-type you may have a different outcome if \( f(3), f(4), ..., f(5) \) data were available.
Thus, above produces no further workings since mapping doesn't correspond; you would need to specify or adjust the function to derive the whole translated table under a composed new set.
To fill in values for x = 5, 2, 1, 0, -1 with some actual functional data for y = f(x + 5), hence the missing functional correlation links need clarify.
To summarize:
- The original table shown has specified points, so deducing from it, we need way to form a valid response - if that helps lead-out any translation that applies.
If more data can amplify that outcome - kindly display shared or specify what's available.