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Trigonometry: Domain, Range, Amplitude, Period

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Trigonometry: Domain, Range, Amplitude, Period

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Questions and Answers

What is the domain of the function $y = -2 ext{sin}(3x + ext{π})$?

All real numbers (correct)

$[0, 2\pi]$

$[-2, 2]$

$(-\infty, \infty)$

What is the range of the function $y = -2 ext{sin}(3x + ext{π})$?

$[-2, 0]$

$[0, -2]$

$[-2, 2]$

$[-3, 0]$ (correct)

What is the amplitude of the function $y = -2 ext{sin}(3x + ext{π})$?

-2

2 (correct)

What is the period of the function $y = -2 ext{sin}(3x + ext{π})$?

<p>$\frac{2\pi}{3}$ (D)</p> Signup and view all the answers

Which of the following statements correctly describes the effect of the negative sign in $y = -2 ext{sin}(3x + ext{π})$?

<p>It reflects the graph over the x-axis. (A)</p> Signup and view all the answers

Flashcards

Domain of y = -2 sin(3x + π)

All real numbers

Range of y = -2 sin(3x + π)

Between -2 and 2

Amplitude of y = -2 sin(3x + π)

Period of y = -2 sin(3x + π)

2π/3

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Phase Shift of y = -2 sin(3x + π)

-π/3

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Study Notes

Domain, Range, Amplitude, and Period of y = -2sin(3x + π)

Amplitude: The amplitude is 2. This is the absolute value of the coefficient of the sine function.
Range: The range of a sine function, whether positive or negative, is from -amplitude to +amplitude. Therefore the range is from -2 to 2.
Period: The period of a sine function is 2π / b, where b is the coefficient of x inside the sine function. In this case, b = 3, so the period is 2π / 3.
Domain: The domain of a sine function is all real numbers. This means the input values (x) can be any real number. This always holds true for any sine function.

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Description

This quiz covers the key concepts of domain, range, amplitude, and period of the sine function. Through understanding the function y = -2sin(3x + π), you will explore these essential topics in trigonometry. Test your knowledge on how these properties relate to sine functions and their graphical representations.