2.) Use the function f(x) = 3 sin C") + 2 to answer parts A-F. (7 Points)
Identify...
F) Graph two full cycles of the function.
A) Equation of the Midline:
B) Amplitude:
C) Max:
D) Min:
E) Period:
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A) y = 2;  B) 3; C) 5; D) 1; E) 2π

Step-by-step explanation:

ƒ(x)=3sinθ + 2

In this function,

3= the amplitude, and

2 = the vertical shift

F) Graph

The figure below shows the graph of your function.

A) Equation of Midline

The midline is the horizontal line that passes through (0,2). Its equation is

ƒ(x) = 2

B) Amplitude

The amplitude is the maximum distance from the midline to the peak or the trough of a wave.

The peaks of your wave are at y = 5 (three units above the midline) and the troughs are at y = -1 (three units below the midline), so

Amplitude = 3

C) Maximum

The maxima are the largest y-values the function can reach (the peaks).

Max = 5

D) Minimum

The minima are the smallest y-values the function can reach (the troughs).

Min = -1

E) Period

The period is the length of one cycle of the curve. It is the distance between two peaks, two troughs, or two crossings of the midline.

Period = 2π ≈ 6.3

what "following statement"?

step-by-step explanation:

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!