Here is the graph of the function $y = -2 \sin(x)$, displaying two complete cycles.

Domain and Range:

• Domain: $(-\infty, \infty)$, as the sine function is defined for all real $x$.
• Range: $[-2, 2]$, since the function oscillates between -2 and 2 due to the amplitude of 2 and the reflection caused by the negative sign.

Would you like further details on interpreting sinusoidal functions or any specific aspects of this graph?

Related Questions:

1. How would the graph change if the amplitude was 3 instead of 2?
2. What effect would a phase shift have on this sine function?
3. How would a vertical shift, such as $y = -2 \sin(x) + 1$, alter the range?
4. Can you identify key points of $y = -2 \sin(x)$ over one period?
5. What would happen to the period if we had $y = -2 \sin(2x)$ instead?

Tip:

For sinusoidal functions, always check amplitude, period, phase shifts, and vertical shifts to understand how the function will appear on the graph.