Understanding the Relationship between a and the Graph of y = f(x): Analyzing Vertical Stretch and Compression

y=af(x), 0

In the given equation, y = af(x), where a is a constant between 0 and 1, and f(x) represents a mathematical function

In the given equation, y = af(x), where a is a constant between 0 and 1, and f(x) represents a mathematical function.

To understand the relationship between a and the graph of y = f(x), let’s analyze some key points:

1. When a = 1:
Since a is equal to 1, the equation simplifies to y = f(x), meaning there is no change to the original function f(x). The graph of y = f(x) remains unchanged.

2. When a is between 0 and 1:
As a decreases from 1 towards 0, the value of y becomes smaller relative to the original function f(x). This implies that the graph of y = af(x) will be compressed vertically towards the x-axis compared to the graph of y = f(x).

3. When a = 0:
When a reaches 0, the equation becomes y = 0 regardless of the value of f(x). This means the graph of y = af(x) will collapse onto the x-axis, resulting in a horizontal line.

In summary, changing the value of a in the equation y = af(x) affects the vertical stretch or compression of the graph of y = f(x). The larger the value of a (closer to 1), the less the compression, while the smaller the value of a (closer to 0), the more compression occurs.

More Answers:

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