The graph y = arctan x is transformed to y = a arctan(b(x-c)) + d by a horizontal compression of 1/4 and a translation of /3 units to the left. The new equation is:

a. y = arctan(4(x+/3))

b. y = 4 arctan(x-/3)

c. y = arctan(1/4(x+/3))

d. y = arctan(4(x-/3))

Describe how the graph of y = 1/5 arccos(-(x+7)) + 2 is a transformation of y = arccos(x).

a. Horizontal Stretch of 5, a reflection about the x-axis, a vertical translation of 2 down, and a horizontal translation of 7 right.

b. Vertical Stretch of 1/5, a reflection about the x-axis, a vertical translation of 7 up, and a horizontal translation of 2 right.

c. Vertical Stretch of 1/7, a reflection about the y-axis, a vertical translation of 2 up, and a horizontal translation of 7 left.

d. Horizontal Stretch of 5, a reflection about the y-axis, a vertical translation of 2 up, and a horizontal translation of 7 left.

At a seaport, the depth of water, h meters, at time t hours, during a certain day is given by:

h(t) = 2.5 sin [2 ((t-4)/(12.4))] + 6.2

What is the maximum depth of the water?

a. 9.2 m

b. 7.7 m

c. 5.2 m

d. 8.7 m

In a certain town in North America, the time of sunrise for any day of the year can be found using the equation:

t = -1.79 sin((2/365)(d - 78)) + 7.3

where tis the time in hours after midnight anddis the number of the day in the year.

To the nearest minute, when did the sun rise on May 7th, the 127th day of the year?

a. 6:23 am

b. 6:05 am

c. 5:58 am

d. 7:23 am