write the equation of the trigonometric function shown in the graph.\n$y = \\cos( x ) + $\nanswer

Explanation:

Step1: Find the amplitude

The amplitude (A) of a cosine function (y = A\cos(Bx)+C) is half the distance between the maximum and minimum values. For the solid - line graph (the function we are interested in), the maximum value (y_{max}=1) and the minimum value (y_{min}=-1). So, (A=\frac{y_{max}-y_{min}}{2}=\frac{1 - (-1)}{2}=1).

Step2: Find the period and (B)

The general formula for the period of a cosine function (y = A\cos(Bx)+C) is (T=\frac{2\pi}{|B|}). For the solid - line graph, the period (T = 2\pi). Using the formula (T=\frac{2\pi}{|B|}), and since (T = 2\pi), we have (2\pi=\frac{2\pi}{|B|}), which gives (|B| = 1).

Step3: Find the vertical shift (C)

The vertical shift (C) of a cosine function (y=A\cos(Bx)+C) is the mid - value between the maximum and minimum values. (C=\frac{y_{max}+y_{min}}{2}=\frac{1+( - 1)}{2}=0).

Answer:

(y = 1\cos(1x)+0)