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

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

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

Answer

Explanation:

Step1: Analyze vertical shift

The black graph (y = \cos x) has a (y -)intercept at ((0,1)). The red graph has a (y -)intercept at ((0,3)).

Step2: Use vertical - shift formula

For a function (y = f(x)+k), the vertical shift is (k). If (y=\cos x) is shifted to (y=\cos x + k), when (x = 0), (y=\cos(0)+k). Since (\cos(0)=1) and (y = 3) (at (x = 0) for the red graph), then (1 + k=3), so (k = 2).

Answer:

(y=\cos(x)+2)