In the form y = a sin(bx - c) + d, which parameter controls horizontal compression or expansion?

• A. a
• B. b
• C. c
• D. d

Answer: (B)

The factor in front of x inside the sine controls horizontal compression or expansion. In y = a sin(bx - c) + d, this is the b that multiplies x. It changes how quickly the sine completes a cycle. The period becomes 2π divided by the absolute value of b. So when |b| > 1, the period shrinks and the graph tightens (horizontal compression); when 0 < |b| < 1, the period stretches (horizontal expansion). The sign of b can also reflect the graph across the y-axis, but the magnitude |b| is what determines compression or expansion. The other parameters affect other aspects: amplitude is scaled by a, horizontal shift (phase) is by c/b, and vertical shift is by d.