Given the function f(x) = log, z, which of the following functions is the transformation of f(x) 9 units down, 5 units left,
reflected across the x-axis, and stretched vertically by a factor of 8? (1 point)
The function f(x) = log, z, can be written as f(x) = log(x).
To find the transformation of f(x) that is 9 units down, we subtract 9 from the function:
f(x) - 9 = log(x) - 9
To find the transformation that is 5 units left, we add 5 to the x variable:
f(x + 5) - 9 = log(x + 5) - 9
To reflect the function across the x-axis, we multiply the function by -1:
-f(x + 5) + 9 = -log(x + 5) + 9
To stretch the function vertically by a factor of 8, we multiply the function by 8:
8(-f(x + 5) + 9) = 8(-log(x + 5) + 9)
Therefore, the transformation of f(x) that is 9 units down, 5 units left, reflected across the x-axis, and stretched vertically by a factor of 8 is:
8(-log(x + 5) + 9)