Final answer:
The parent function of sine looks like a wave oscillating between -1 and 1, with a full cycle every 2π radians. In the function f(x) = a sin(bx), the 'a' value determines the amplitude of the wave, which is the maximum distance from the wave's centerline to its peak or trough.
Step-by-step explanation:
The parent function of sine is represented by the mathematical function f(x) = sin(x). This function produces a wave that oscillates between -1 and 1, and it completes a full cycle every 2π radians.
In the function f(x) = a sin(bx), the 'a' value represents the amplitude of the sine wave. The amplitude is the maximum distance from the wave's rest position (the horizontal axis) to its peak (either the top or bottom of the wave). Therefore, an 'a' value in this function affects how large or small the peaks and troughs of the sine wave are.
Considering the options provided: a. Amplitude, b. Period, c. Phase shift, d. Vertical translation, the 'a' value corresponds to option a, which is the Amplitude.