Final answer:
The correct transformation of the logarithmic parent function is f(x) = -8 * log₂(x + 2), after it is vertically stretched by a factor of 8, reflected across the x-axis, and translated left 2 units. The resulting function is option (a).
Step-by-step explanation:
If the logarithmic parent function, f(x) = log₂(x), undergoes a series of transformations, starting with a vertical stretch by a factor of 8, followed by a reflection across the x-axis, and ending with a translation 2 units to the left, the resulting function will incorporate these changes step by step.
To vertically stretch the function by a factor of 8, we simply multiply the original function by 8:
f(x) = 8 ∙ log₂(x).
Next, reflecting it across the x-axis involves multiplying the function by -1:
f(x) = -1 ∙ 8 ∙ log₂(x) or f(x) = -8 ∙ log₂(x).
Lastly, translating it left by 2 units means we substitute x in the function with (x+2):
f(x) = -8 ∙ log₂(x+2).
Therefore, the correct transformation of the given logarithmic parent function is f(x) = -8 ∙ log₂(x+2), which matches option (a).