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1.  2.  3. 4. 5. 6. 7. Jan 29, 2018

#1
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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   Jan 29, 2018
#2
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3.

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

Shifted down 2 units gives  y  =  -cos(x) - 2 = g(x)   Jan 29, 2018
#3
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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   Jan 29, 2018
#4
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5.

We can solve for the period, p,  as follows

(1/4) p  = 2pi      multiply both sides by 4

p   =  8 pi

The frequency  =  1 / period  =    1  / [ 8 pi ]   Jan 29, 2018
#5
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6. The period is  pi / 2

7.  The graph is vertically stretched by a factor of 2  and shifted up 3 units   Jan 29, 2018