the function graphed to the right is of the form y = c + cos x, y = c + sin x, y = cos (x - d), or y = sin…

the function graphed to the right is of the form y = c + cos x, y = c + sin x, y = cos (x - d), or y = sin (x - d), where d is the least possible positive value. determine the equation of the graph. y = (type an expression using x as the variable.)

the function graphed to the right is of the form y = c + cos x, y = c + sin x, y = cos (x - d), or y = sin (x - d), where d is the least possible positive value. determine the equation of the graph. y = (type an expression using x as the variable.)

Answer

Explanation:

Step1: Determine the vertical - shift

The maximum value of the function is 3 and the minimum is 1. The mid - line is $y=\frac{3 + 1}{2}=2$. So, $c = 2$.

Step2: Identify the type of trigonometric function

The graph looks like a cosine function. The general form of a cosine function is $y = c+\cos(x - d)$. When $x = 0$, the function is at its maximum value. For $y=\cos(x - d)$, when $x = 0$, $y=\cos(-d)=\cos(d)$. Since the function starts at its maximum, $d = 0$.

Answer:

$y = 2+\cos x$