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# Determine a function that could be represented by the following graphs.

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

Dec 10, 2017
edited by Guest  Dec 10, 2017

#1
+95966
+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

Dec 10, 2017
#2
+95966
+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

Dec 10, 2017
edited by CPhill  Dec 10, 2017
#3
+95966
+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

Dec 10, 2017
#4
+95966
+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

Dec 10, 2017