# (cos x) - Periodicity and other simple properties of functions

- Author:
- Megan Dunford

- Topic:
- Functions

In exercise 5.7 and 5.8 you looked and the periodicity and other simple properties of functions.
Where,
has amplitude 1 and period
has amplitude 1 and period
has no amplitude and period
In this GeoGebra you are going to look at the different properties and periodicity of each function and what happens when you alter the functions with different functions

## Periodicity and other simple functions of the function f(x)= cos (x)

has amplitude and period
Have a play with the GeoGebra below. Notice what starts to happen when you move the sliders

## Amplitude of the function f(x) = cos(x)

Explain what happens to the function f(x) = cos(x) as the amplitude increases from 0 to 5. Use examples of what the amplitude is like at a = 2 and a = 5.

## Amplitude of the function f(x) = cos(x)

Explain what the difference is when the amplitude is positive or negative to the function f(x) = cos(x). Does this impact the function? Use examples of what the amplitude is like at a = -3 and a = 3

## Period of the function f(x) = cos(x)

Explain what happens to the function f(x) = cos(x) when the period is positive at . (Hence the slider = 4)

## Period of the function f(x) = cos(x)

Explain what happens to the period of the function f(x) = cos(x) between -1 and -5. How does the negative period affect the function?