Answer:
y = 1 +cos(3/2(x+π/3))
Explanation:
You want the equation of a cosine graph.
Transformations
The usual transformations applied to a parent function are ...
- a·f(x) — vertical expansion by a factor of 'a'
- f(x-h) +k — translation by h units right and k units up
- f(x/a) — horizontal expansion by a factor of 'a'
Vertical scale factor
The difference between the maximum and minimum of a cosine function is (1) -(-1) = 2. We observe that same difference on this graph, so there is no vertical scaling.
Translation
The maximum of a cosine function is found at (0, 1). On this graph, the nearest maximum is at (-π/3, 2). Subtracting the usual location gives the values of the horizontal and vertical translation:
(h, k) = (-π/3, 2) - (0, 1) = (-π/3, 1)
Horizontal scale factor
The period (from one peak to the next) of the graph is π -(-π/3) = 4π/3. The usual period of the cosine function is 2π, so this graph has been "expanded" by the factor (4π/3)/(2π) = 2/3.
Equation
Putting these transformations into the equation for the cosine function, we get ...
y = cos((x -(-π/3))/(2/3)) +1
y = 1 +cos(3/2(x +π/3)) . . . . equation of the graph
You can eliminate the inner parentheses by writing this in the equivalent form ...
y = 1 +cos(3/2x + π/2)