Find a function of the form y= A sin (kx) + C or y= A cos (kx) + C whose graph matches this one:

Question

Can someone pleaseeee help me figure out the function to this graph? I've been stuck on this for a while. Helpppp pleaseee.

I'm extremely confused.

Here's a link to a photo of the graph:

https://ibb.co/HDS2g8K

Answer 1

Hi Vaniesha,

1. The graph crosses the y-axis at the max amplitude of A = 5, so easier to use to COSINE equation.

1. To find C: C is the midline = (maximum + minimum)/2 = (5 + -5)/2 = 0/2 = 0

1. k = 2pi/Period; period = spacing between repeating patterns. There are 14 units between each peak (peak when x = -14, next peak when x = 0). So: k = 2pi/14 = pi/7

recap: A = 5, C = 0, k = pi/7, graph crosses y-axis at max amplitude so cosine makes most sense. Therefore:

y = 5 cos(pi*x/7)