Question

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

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:

\(y=\cos(x)+2\)