#1**0 **

1. Minimum value is 2.5

2. Period = 6pi Amplitude = 5 Midline : y = -2

Since we have a y intercept of (0, -2) the sine function seems he best choice...here's the function :

y = 5sin (x /3 ) - 2

Here's the graph : https://www.desmos.com/calculator/shtgla34yy

CPhill Jan 29, 2018

#2**0 **

3.

Reflected over the x axis gives us y = -cos (x)

Shifted down 2 units gives y = -cos(x) - 2 = g(x)

CPhill Jan 29, 2018

#3**0 **

4. f(x) = (1/2)cos ( x) + 5

The "1/2 " does not affect the midline..it only halves the normal amplitude

The "5" shifts the normal cosine graph up 5 uints

So....the midline is y = 5

Here's the graph : https://www.desmos.com/calculator/lkmkkpvrzq

CPhill Jan 29, 2018