Which of the following equations matches the function shown above?

C=y=sin1/2x

Step-by-step explanation:

As given in the graph:

Amplitude= 1

period=2π

Finding function of sin that have period of 4π and amplitude 1

A: y=1/2sinx

Using the formula  asin(bx-c)+d to find the amplitude and period

a=1/2

b=1

c=0

d=0

Amplitude=|a|

                =1/2

Period= 2π/b

         =2π

B: y=sin2x

Using the formula  asin(bx-c)+d to find the amplitude and period

a=1

b=2

c=0

d=0

Amplitude=|a|

                =1

Period= 2π/2

         =π

C: y=sin1/2x

Using the formula  asin(bx-c)+d to find the amplitude and period

a=1

b=1/2

c=0

d=0

Amplitude=|a|

                =1

Period= 2π/1/2

         =4π

D: y=sin1/4x

Using the formula  asin(bx-c)+d to find the amplitude and period

a=1

b=1/4

c=0

d=0

Amplitude=|a|

                =1

Period= 2π/1/4

         =8π

Hence only c: y=sin1/2x has period of 2π and amplitude 1

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: