Which function has the given properties? The domain is the set of all real numbers. One x -intercept is open paren 2 pi comma 0 close paren The amplitude is 4 The point open paren pi over 2 comma negative 4 close paren is on the graph. The y -intercept is open paren 0 comma 0 close paren

An amplitude of 4 means the sine or cosine coefficient has magnitude 4. Since the graph passes through (π/2, −4), the function must give −4 when x = π/2; −4 sin(π/2) = −4. The function y = −4 sin x also has y-intercept 0 and an x-intercept at x = 2π, so choice B, y = −4 sin x, matches all the properties.

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