To determine which function has been vertically stretched by a factor of 8 and reflected across the x-axis, we need to evaluate the required transformations:
-
Vertically stretched by a factor of 8: This means we multiply the function by 8. If the original function is \( f(x) \), then the vertically stretched function would be \( 8f(x) \).
-
Reflected across the x-axis: This means we multiply the entire function by -1. Therefore, the function after reflection would be \( -8f(x) \).
Combining both transformations, we can summarize that the resulting function would be \( -8f(x) \).
Now let's analyze the provided options based on the transformations we've described:
-
Option 1: \( f(x) = 8|x| \)
- This is stretched but not reflected.
-
Option 2: \( f(x) = -18|x| \)
- This appears to be stretched (by a factor of 18) and reflected, but the stretch factor is not 8.
-
Option 3: \( f(x) = 18|x| \)
- This is stretched by a factor of 18 and not reflected.
-
Option 4: \( f(x) = -8|x| \)
- This function is both reflected across the x-axis and vertically stretched by a factor of 8.
Thus, the correct answer is:
f(x) = -8|x|