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Two Quick Questions

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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).

Guest Feb 17, 2018
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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)

CPhill  Feb 17, 2018

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