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The family of curves given by y = a sin(bx) is characterized by:

Practice Questions

Q1
The family of curves given by y = a sin(bx) is characterized by:
  1. Linear behavior
  2. Periodic behavior
  3. Exponential growth
  4. Quadratic growth

Questions & Step-by-Step Solutions

The family of curves given by y = a sin(bx) is characterized by:
  • Step 1: Identify the equation y = a sin(bx).
  • Step 2: Recognize that 'a' affects the height of the curve (amplitude).
  • Step 3: Understand that 'b' affects the width of the curve (frequency).
  • Step 4: Note that the sine function is periodic, meaning it repeats its values in regular intervals.
  • Step 5: Conclude that changing 'a' and 'b' will create different curves, but they will all be periodic.
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