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[br]
[math]y=a\cdot tan\left(bx\right)[/math] has no amplitude and period [math]\frac{\pi}{b}[/math].[br]Have a play with the GeoGebra below. Notice what happens to the period when you move the sliders
Explain why the function f(x) = tan(x) has no amplitude
Explain what happens to the function f(x) = tan(x) when the period (b) is [math]\frac{\pi}{1}[/math]. (Hence when the slider =1)
Explain what happens to the function f(x) when the period (b) is [math]\frac{\pi}{5}[/math]. (Hence when the slider =5)
Explain what happens to the function f(x) when the period (b) is [math]\frac{\pi}{-3}[/math]. (Hence when the slider =-3)