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The family of curves given by y = a sin(bx) is characterized by:
The family of curves given by y = a sin(bx) is characterized by:
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Practice Questions
1 question
Q1
The family of curves given by y = a sin(bx) is characterized by:
Linear behavior
Periodic behavior
Exponential growth
Quadratic growth
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The equation y = a sin(bx) represents a family of periodic curves.
Questions & Step-by-step Solutions
1 item
Q
Q: The family of curves given by y = a sin(bx) is characterized by:
Solution:
The equation y = a sin(bx) represents a family of periodic curves.
Steps: 5
Show Steps
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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