Which of the following represents a family of curves for the equation y = a sin(

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Question: Which of the following represents a family of curves for the equation y = a sin(bx)?

Options:

Correct Answer: Sine waves with varying amplitudes and frequencies

Solution:

The equation y = a sin(bx) represents sine waves where \'a\' is the amplitude and \'b\' is the frequency.

Which of the following represents a family of curves for the equation y = a sin(bx)?

Which of the following represents a family of curves for the equation y = a sin(bx)?

Correct Answer: y = a sin(bx)

Step 1: Understand the equation y = a sin(bx).
Step 2: Identify 'a' in the equation. This represents the amplitude, which is the height of the wave from the center line.
Step 3: Identify 'b' in the equation. This represents the frequency, which affects how many waves fit into a certain distance.
Step 4: Realize that changing 'a' will make the waves taller or shorter, while changing 'b' will make the waves closer together or further apart.
Step 5: Recognize that different values of 'a' and 'b' create different sine waves, forming a family of curves.

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