In exercise 5.7 and 5.8 you looked and the periodicity and other simple properties of functions. [br]Where,[br][math]y=sin\left(x\right)[/math] has amplitude 1 and period [math]2\pi[/math][br][math]y=cos\left(x\right)[/math] has amplitude 1 and period [math]2\pi[/math][br][math]y=tan\left(x\right)[/math] has no amplitude and period [math]\pi[/math][br][br]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
[math]y=a\cdot cos\left(bx\right)[/math] has amplitude [math]a[/math] and period [math]\frac{2\pi}{b}[/math][br]Have a play with the GeoGebra below. Notice what starts to happen when you move the sliders
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.
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
Explain what happens to the function f(x) = cos(x) when the period is positive at [math]\frac{2\pi}{4}[/math]. (Hence the slider = 4)
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?