The diagram below shows the graph of the function $f : x ightarrow ext{sin } 2x$ - Leaving Cert Mathematics - Question 5 - 2014

Graph of $g(x) = \text{sin } x$:

• The sine function oscillates between -1 and 1.
• It completes one full period from 0 to $2\pi$. In this interval, the graph will rise to 1 at $\frac{\pi}{2}$ and then fall back to -1 at $\frac{3\pi}{2}$.
• This graph should be drawn in green.

Graph of $h(x) = 3\text{sin } 2x$:

• This function has an amplitude of 3 and will oscillate between -3 and 3.
• It completes one full cycle in the interval from 0 to $\pi$, with the peaks occurring at $\frac{\pi}{4}$ and $\frac{3\pi}{4}$.
• This graph should be drawn in red.

Labeling:

• Clearly indicate which graph is for $g$ (green) and which is for $h$ (red) on the diagram.