the black graph is y = cos x. choose the equation for the red graph. (0,1) (0,3) y = cos(x) + 2 y = cos(x…

the black graph is y = cos x. choose the equation for the red graph. (0,1) (0,3) y = cos(x) + 2 y = cos(x - π/2) y = cos(x + π) y = cos(x) - 1

the black graph is y = cos x. choose the equation for the red graph. (0,1) (0,3) y = cos(x) + 2 y = cos(x - π/2) y = cos(x + π) y = cos(x) - 1

Answer

Explanation:

Step1: Recall vertical shift formula

For (y = f(x)+k), (k) is vertical shift. If (k>0), shift up; if (k < 0), shift down.

Step2: Analyze the (y -) intercepts

For (y=\cos(x)), when (x = 0), (y=\cos(0)=1). For the red graph, when (x = 0), (y = 3). Let (y=\cos(x)+k). Substitute (x = 0), (y = 3) into (y=\cos(x)+k). We get (3=\cos(0)+k). Since (\cos(0)=1), then (3 = 1 + k), so (k=2).

Answer:

(y=\cos(x)+2)