Example: Amplitude and period transformations  Trigonometry  Khan Academy  Summary and Q&A
TL;DR
Graphing the function y = 2sin(x) involves reflecting and doubling the amplitude of the sine function.
Questions & Answers
Q: How does multiplying the function by 2 affect the graph of y = 2sin(x)?
Multiplying the function by 2 doubles the amplitude of the graph, making it oscillate between 2 and 2 instead of 1 and 1.
Q: What happens when sin(x) is graphed on the interval 2π to 2π?
The graph of sin(x) follows a typical sine wave pattern, starting at 0, reaching a maximum amplitude of 1, returning to 0, and then reaching a minimum amplitude of 1.
Q: How does graphing sin(x) differ from graphing sin(x)?
Graphing sin(x) reflects the graph over the yaxis, resulting in a mirrored image of the original graph. The function values remain the same, but in a different order.
Q: What is the period of the function y = 2sin(x)?
The period of y = 2sin(x) is the same as the period of sin(x), which is 2π. The negative in front of x does not affect the period.
Summary & Key Takeaways

Graphing y = sin(x) on the interval 2π to 2π shows a typical sine wave pattern.

Multiplying the function by 2 results in doubling the amplitude of the graph.

Graphing y = sin(x) reflects the graph over the yaxis.