Question

You may use Desmos. Please box your answers, so they are easy to find. Combine both pages into one document. This must be printed out and handwritten to be accepted! 1.) Use the graph below to answer parts A – G. (7 Points) Identify… A) Max: B) Min: C) Equation of the Midline: D) Amplitude: E) Period: F) Frequency: G) What is the equation of the sinusoid? () = 2.) Use the function () = 3 sin � 2 � + 2 to answer parts A - F. (7 Points) Identify… A) Equation of the Midline: B) Amplitude: C) Max: D) Min: E) Period:

Answer 1

Answer:

See explanation

Step-by-step explanation:

1. For the given graph:

A. Max is at -1 and

B. Min is at -5.

C. The midline of a sinusoidal function is the horizontal center line about which the function oscillates above and below. Hence, the midline has the equation

$y=\dfrac{Max+Min}{2}=\dfrac{-1+(-5)}{2}=\dfrac{-6}{2}=-3$

D. The amplitude of a sinusoidal function is one-half of the positive difference between the maximum and minimum values of a function, so

$Amplitude=\left|\dfrac{-1-(-5)}{2}\right|=2$

E. The period of a periodic function is the horizontal length of one complete cycle (the distance between two consecutive maximums), then the period is

$\dfrac{3\pi}{2}-\dfrac{\pi}{2}=\pi$

F. The frequency of a trigonometric function is the number of cycles it completes in a given interval. This interval is generally 2π radians (or 360º) for the sine and cosine curves. Actually,

$Frequency=\dfrac{2\pi }{\pi}=2$

G. The equation of the function is

$f(x)=2\sin \left(2\left(x-\dfrac{\pi}{2}\right)\right)-3$

2. For the given function $f(x)=3\sin \left(\dfrac{\pi x}{2}\right)+2$

A. Max is at 5 and

B. Min is at -1.

C. The midline of a sinusoidal function is the horizontal center line about which the function oscillates above and below. Hence, the midline has the equation

$y=\dfrac{Max+Min}{2}=\dfrac{5-1}{2}=\dfrac{4}{2}=2$

D. The amplitude of a sinusoidal function is one-half of the positive difference between the maximum and minimum values of a function, so

$Amplitude=\left|\dfrac{5-(-1)}{2}\right|=3$

E. The period of a periodic function is the horizontal length of one complete cycle (the distance between two consecutive maximums), then the period is

$|5-1|=4$

F. The frequency of a trigonometric function is the number of cycles it completes in a given interval. This interval is generally 2π radians (or 360º) for the sine and cosine curves. Actually,

$Frequency=\dfrac{2\pi }{4}=\dfrac{\pi}{2}$

G. The graph of the function is attached.