Question

which of the following graphs represents the function y = -3 sin (x + π/4) + 1? a)

Explanation:

Step1: Identify amplitude

The general form of a sinusoidal function is $y = A\sin(Bx - C)+D$. For $y=-3\sin(x + \frac{\pi}{4})+1$, the amplitude $|A| = |- 3|=3$. This means the graph oscillates between $y = 1 + 3=4$ and $y=1 - 3=-2$. Option A has an amplitude of 2 (oscillates between $y = 2$ and $y=-2$), while option B has an amplitude of 3 (oscillates between $y = 4$ and $y=-2$).

Step2: Identify vertical - shift

The value of $D$ in the function $y=-3\sin(x+\frac{\pi}{4})+1$ is 1, which means the graph is shifted 1 unit up from the standard sine - wave position. Option B shows a vertical shift such that the mid - line of the wave is at $y = 1$.

Answer:

B.