Title says it all.. What would the corresponding functions be for these four graphs?

UpTheChels
Dec 10, 2017

edited by
Guest
Dec 10, 2017

#1**+2 **

First one....one possibility

Midline = -1

Amplitude = 2

Vertical shift down 1

Phase shift.....sine curve shifted to the right by 3pi/4 units

1 period in 2pi [ normal period ]

So the equation is :

y = 2sin(x - 3pi/4) - 1

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

CPhill
Dec 10, 2017

#2**+2 **

Second one......one possibility

Midline = .6

Vertical shift is up .6 units

Amplitude = .3

Period = pi....so....2 periods in 2 pi

Phase shift....sine graph shifted to the right by 3pi/4 units

The equation is

y = .3sin2(x - 3pi/4) + .6

Here's the graph : https://www.desmos.com/calculator/vr3zoak70p

CPhill
Dec 10, 2017

#3**+2 **

Third one....this one is easier

Midline = 0

No vertical shift

Amplitude = 2

Period = pi....so....2 periods in 2 pi

Phase shift....sine curve shifted to the left by pi/6 units

So.....the equation is

y = 2sin2(x + pi/6)

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

CPhill
Dec 10, 2017

#4**+2 **

Last one......pretty easy, too

Midline = 0

No vertical shift

Amplitude = .5

Period = 4pi....so (1/2) periods in 2pi

Sine curve shifted to the right by pi units

The equation is :

y = .5sin (1/2)(x - pi) = .5sin ( [ x - pi ] / 2 )

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

CPhill
Dec 10, 2017