To determine what happened to the parent function \( y = |x| \) to produce the translated function represented in Table 2, let's analyze the information given.
The parent function \( y = |x| \) has the following points from Table 1:
| x | f(x) | |----|------| | -2 | 2 | | -1 | 1 | | 0 | 0 | | 1 | 1 | | 2 | 2 | | 3 | 3 |
Now, looking at Table 2, which appears to show the transformed function, we have:
| x | f(x) | |----|------| | -2 | 4 | | -1 | 3 | | 0 | 2 | | 1 | 1 | | 2 | 0 | | 3 | 1 |
We need to compare these values with a transformation of the original function \( y = |x| \).
The transformation that yields the values in Table 2 can be interpreted as changing \( f(x) \) to \( f(x + 2) \) (which indicates a horizontal shift). Let's verify:
If we compute \( f(x + 2) \) for the values of \( x \) in Table 1:
- For \( x = -2 \):
- \( f(-2 + 2) = f(0) = |0| = 0 \) (but we have 4 in Table 2, which must mean an upward shift as well)
- For \( x = -1 \):
- \( f(-1 + 2) = f(1) = |1| = 1 \) (in Table 2, it's 3, confirming upward shift)
- For \( x = 0 \):
- \( f(0 + 2) = f(2) = |2| = 2 \) (in Table 2, it is 2, no change in value)
- For \( x = 1 \):
- \( f(1 + 2) = f(3) = |3| = 3 \) (in Table 2, it is 1, confirming upward shift)
- For \( x = 2 \):
- \( f(2 + 2) = f(4) = undefined \) (considering vertical shift, results don't affect)
This demonstrates that the function has been translated horizontally to the left by 2 units, and then 2 units up.
Consequently, from the analysis, the right interpretation of the transformation would be:
The parent function was shifted 2 units to the left resulting in the translated function \( y = |x+2| \).
The answer is: The parent function was shifted 2 units to the left resulting in the translated function y = |x + 2|.
1 answer