which of the functions is graphed?\n$y = - 0.5\\cos(x)-1$\n$y=-0.5\\sin(x)+1$\n$y = 0.5\\sin(x)-1$\n$y =…

which of the functions is graphed?\n$y = - 0.5\\cos(x)-1$\n$y=-0.5\\sin(x)+1$\n$y = 0.5\\sin(x)-1$\n$y = 0.5\\cos(x)+1$\ndone

which of the functions is graphed?\n$y = - 0.5\\cos(x)-1$\n$y=-0.5\\sin(x)+1$\n$y = 0.5\\sin(x)-1$\n$y = 0.5\\cos(x)+1$\ndone

Answer

Explanation:

Step1: Analyze the y - intercept

When (x = 0), for (y=-0.5\cos(x)-1), (y=-0.5\times1 - 1=-1.5); for (y=-0.5\sin(x)+1), (y = 1); for (y = 0.5\sin(x)-1), (y=-1); for (y = 0.5\cos(x)+1), (y=0.5\times1 + 1 = 1.5). The graph has a y - intercept around (y = 1).

Step2: Analyze the general shape

The standard form of a sine function is (y = A\sin(x)+k) and cosine function is (y=A\cos(x)+k). The graph looks like a sine - type function (starts at non - maximum/minimum value at (x = 0)). The amplitude (|A|) and vertical shift (k) also matter. The graph has an amplitude of (0.5) and a vertical shift of (1) upwards. The function (y=-0.5\sin(x)+1) satisfies these characteristics.

Answer:

(y=-0.5\sin(x)+1)