To translate the function \( y = f(x) \) to \( y = f(x + 5) \), we apply a horizontal shift. Specifically, the "+5" inside the function indicates that we shift the graph of \( f(x) \) to the left by 5 units.
Given the original function \( y = f(x) \) with the specified values:
- When \( x = -2 \), \( y = f(-2) \)
- When \( x = -1 \), \( y = f(-1) \)
- When \( x = 0 \), \( y = f(0) \)
- When \( x = 1 \), \( y = f(1) \)
- When \( x = 2 \), \( y = f(2) \)
To find the corresponding values for the translated function \( y = f(x + 5) \), we calculate:
- When \( x = -7 \), \( y = f(-2) \) (because \(-7 + 5 = -2\))
- When \( x = -6 \), \( y = f(-1) \) (because \(-6 + 5 = -1\))
- When \( x = -5 \), \( y = f(0) \) (because \(-5 + 5 = 0\))
- When \( x = -4 \), \( y = f(1) \) (because \(-4 + 5 = 1\))
- When \( x = -3 \), \( y = f(2) \) (because \(-3 + 5 = 2\))
Here’s the translated function's values relative to original values:
- \( x = -7 \) gives \( y = f(-2) \)
- \( x = -6 \) gives \( y = f(-1) \)
- \( x = -5 \) gives \( y = f(0) \)
- \( x = -4 \) gives \( y = f(1) \)
- \( x = -3 \) gives \( y = f(2) \)
Effectively, you would replace each \( x \) value by adding 5 to the shifted function’s input, moving all values to the left by 5 on the x-axis.
If you need further details about the function, values for \( f(x) \), or specific calculations, please provide those, and I can help with that too!