Question: The family of curves given by y = a sin(bx) is characterized by:
Options:
Linear behavior
Periodic behavior
Exponential growth
Quadratic growth
Correct Answer: Periodic behavior
Solution:
The equation y = a sin(bx) represents a family of periodic curves.
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:
Linear behavior
Periodic behavior
Exponential growth
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.
Periodic Functions – The equation y = a sin(bx) represents a family of periodic functions, where 'a' affects the amplitude and 'b' affects the frequency.
Amplitude and Frequency – The parameter 'a' determines the height of the wave (amplitude), while 'b' determines how many cycles occur in a given interval (frequency).
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