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What type of curves does the equation y = a sin(bx + c) represent?

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Question: What type of curves does the equation y = a sin(bx + c) represent?

Options:

  1. Linear functions
  2. Exponential functions
  3. Trigonometric functions
  4. Polynomial functions

Correct Answer: Trigonometric functions

Solution: 

The equation y = a sin(bx + c) represents a family of trigonometric functions (sine waves) with varying amplitude (a) and frequency (b).

What type of curves does the equation y = a sin(bx + c) represent?

Practice Questions

Q1
What type of curves does the equation y = a sin(bx + c) represent?
  1. Linear functions
  2. Exponential functions
  3. Trigonometric functions
  4. Polynomial functions

Questions & Step-by-Step Solutions

What type of curves does the equation y = a sin(bx + c) represent?
Correct Answer: Sine waves
  • Step 1: Identify the equation given, which is y = a sin(bx + c).
  • Step 2: Recognize that this equation represents a sine wave, which is a type of curve.
  • Step 3: Understand that 'a' affects the height of the wave, known as amplitude.
  • Step 4: Realize that 'b' affects how many waves fit into a certain distance, known as frequency.
  • Step 5: Note that 'c' shifts the wave left or right, changing its starting point.
  • Step 6: Conclude that the equation describes a family of sine waves with different heights and frequencies.
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