Question

Find an equation for the given graph.

Answer 1

y = -3 sin(4x)

or

y = -3 cos(4(x - π/8))

Explanation:

We can see that this is a graph of sine or cosine with the following characteristics:

amplitude: 3

period: π/2

vertical shift: 0

We can use these characteristics to form the following equations:

y = -3 sin(4x)

y = -3 cos(4(x - π/8))

Note that we solved for b using the period derivation:

period = 2π / b

`(\pi)/(2) = (2\pi)/(b)`

`b \cdot (\pi)/(2) = 2\pi}`

`b = 2\pi \cdot (2)/(\pi)`

`b = (4\pi)/(\pi)`

`b = 4`

— sidenote —

These graphs can be infinitely shifted by any integer number of periods left or right, and we can show that using an auxiliary variable multiplied by the period. However, that is clearly not the intent of the problem, so I have not included that in my answer.