1. What is the minimum value for the function shown in the graph?
2. Graph a sine function whose amplitude is 5, the period is 6π, midline is y=−2, and the y-intercept is (0, −2). The graph is not a reflection of the parent function over the x-axis.
The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
(Please explain the coordinates of the first point-the midline and the coordinates of the second point).
1. Minimum value is y = -6
2. In the form y = Asin(Bx) + C
A = 5
Since the y intercept is (0, - 2), C is -2
To find B we need to solve this
B = [ 2pi ] / period = [ 2pi ] / [ 6 pi] = 1/3
So....the function is :
y = 5sin ( (1/3) x ) - 2
Here's the graph : https://www.desmos.com/calculator/0s8smsawk2
The midlne is y = -2
The first point on the midline is (0, - 2)
The next point [to the right of the first point ] is a max at (3pi/2, 3)