Question

Find a function of the form y = A * sin(kx) + C Cory y = A * cos(kx) + C whose graph matches the function shown below:

Answer 1

we have the equation of the form

`y=Asin(kx)+C`

Find out the value of A (amplitude)

The Amplitude is the height from the center line to the peak (or to the trough). Or we can measure the height from highest to lowest points and divide that by 2

A=(4+8)/2=6

A=6

Find out the Period

Period=2pi/k

The Period goes from one peak to the next (or from any point to the next matching point)

so

Period=10.5+3.5=14

14=2pi/k

k=2pi/14

k=pi/7

Find out the value of C

The Vertical Shift is how far the function is shifted vertically from the usual position

Looking at the graph

the center line is at y=-2

C=-2

substitute given values

`y=6sin((\pi)/(7)x)-2`