Example: Amplitude and period transformations | Trigonometry | Khan Academy | Summary and Q&A

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May 27, 2015
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Example: Amplitude and period transformations | Trigonometry | Khan Academy

TL;DR

Graphing the function y = 2sin(-x) involves reflecting and doubling the amplitude of the sine function.

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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 y-axis, 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 y-axis.

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