# How do you graph #y=2sin(x/2)#?

##### 1 Answer

May 14, 2018

Vertical and horizontal stretches.

#### Explanation:

Starting from the standard sine function

#sin(x) \to sin(x/2)# . Multipling the input variable means to horizontally stretch/compress the graph of the function. So, in general,#f(x) \to f(kx)# means to compress the graph if#|k|>1# , and stretch it otherwise. Since in your case#k = 1/2# , the graph will be stretched by a factor of#2# . This means, for example, that the sinusoidal waves will take twice the time to complete their oscillations.- Then, you have
#sin(x/2) \to 2sin(x/2)# . This kind of transformations#f(x) \to kf(x)# result in a vertical stretch if#|k|>1# , or a vertical compression otherwise. Since in your case#k=2# , the graph will be vertically stretched, again by a factor of#2# . This affects the amplitude of the waves, which will no longer range between#-1# and#1# , but between#-2# and#2# .

Here you can see the two graphs drawn together.