Final answer:
The statement is false as the correct application of the distributive property should apply 'k' to both 'x' and '-b', thus not simplifying to 'y = asin(kx - kb)'.
Step-by-step explanation:
The student's question pertains to understanding the correctness of a sine function's equation transformation. Specifically, it checks if the equation y = asin(k(x-b)) is equivalent to y = asin(kx - kb).
To address this, consider the original sine function with a phase shift. The correct transformation of the function y = asin(k(x-b)) involves taking 'b' outside of the sine function while keeping the 'k' inside, which means it should be y = asin(kx - kb) assuming 'a' and 'k' are constants and 'b' is the phase shift. Thus, the statement is False, because when you expand 'k(x-b)', you should distribute the 'k' across both 'x' and '-b', not just 'x'.