Question

2. (12 points) For each of the following generalized sine or cosine functions, properly identify the coefficients A, B,C and D and then find: the domain and the range, the

amplitude, the period, the phase shift, the vertical shift, and a full-cycle interval. Then, sketch the graph of the function on the full-cycle interval,by showing clearly the key-points of the function on that interval (these are the zeroes/x-intercepts, and the relative minima/maxima). (a) (3 points) f(r) = 3 sin(4x – 2). (b) (3 points) f (x) = -2 cos(3r) + 1. (Recall that, when A < 0, we also have a reflection about the x-axis of the graph of f(x) with respect to the graph of sin(x).) \text { (c) (3 points) } f(x)=\sin \left(\frac{\pi x}{4}-\frac{\pi}{2}\right)-1 \text { . } \text { (d) }(3 \text { points }) f(x)=\frac{1}{2} \cos \left(-\left(\frac{\pi x}{3}+\frac{\pi}{6}\right)\right)+2 . \text { (Recall that } \left.\cos (-x)=\cos (x) \ldots\right)

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