Question

What is the equation of the following graph?

https://static.k12.com/eli/bb/179/5_17041/2_7373_6_17083/24fe291733623116e1abe17dcf3ca46d51cc325a/media/06c926c9bcb68b724686bea62ef4b08adfe94de7/mediaasset_669547_1.gif

Answer 1

May I help?

Answer 2

so this a trig function. As you can see the y intercept is at 1. This tells you it is probably related to the cosine function.

so your graph will be on the form y = a cos (bx) where a is the amplitude, and b is the period factor.
As you complete one cycle of the graph from x = 0 to x = 2 pi the period is 2pi (distance to complete one cycle). Also the period, T, is linked to the period factor, b, given by this formula:
\[T = \frac{ 2\pi }{ b }\]
T = 2 pi/b = 2pi so b = 1
Amplitude is your y intercept of 1.
put this together now...