Question

When b= 0.5, the period of orange graph is _ pi

When b= 2, the period of orange graph is _ pi

Answer 1

Part 2:

Based on this evidence,

When b > 1, the period

✔ decreases

.

When 0 < b < 1, the period

✔ increases

Explanation:

This is correct for edge 2020. Hope this helps someone.

Answer 2

When b= 0.5, the period of orange graph is _4_ pi

When b= 2, the period of orange graph is _1_pi

Explanation:

The period of the sinusoidal functions can be easily calculated by observing their graphs.

First, look at the orange graph when b = 0.5

Identify a point where the orange chart cuts the x-axis. For example at
`x = 0`. After completing the rise and fall cycle, the function cuts back to the x axis at
`x = 4\pi`.

Then the period
`T = 4\pi`.

Second, look at the orange graph when b = 2

Identify a point where the orange chart cuts the x-axis. For example at
`x = 0`. After completing the rise and fall cycle, the function cuts back to the x-axis at
`x = \pi`.

Then the period
`T = \pi`.

We also know that the period of a sinusoidal function is defined as
`T(b) = (2\pi)/(b)`

So:

`T(0.5) = (2\pi)/(0.5) = 4\pi\\\\T(2) = (2\pi)/(2) = \pi`