Understanding Vertical Stretch | Exploring the Effects of Multiplying a Function by a Constant Greater than 1

y=af(x) a>1

In the given equation, y = af(x), where a is a constant greater than 1, we are dealing with a transformation of the function f(x)

In the given equation, y = af(x), where a is a constant greater than 1, we are dealing with a transformation of the function f(x).

A transformation of a function involves modifying the original function in some way, such as stretching or compressing, reflecting, or translating it. In this case, we are multiplying the function by a constant ‘a’ that is greater than 1.

When ‘a’ is greater than 1, it causes a vertical stretch. This means that each y-coordinate of the original function gets multiplied by a. The x-coordinate remains unaffected.

To better understand how this transformation works, let’s consider an example:

Suppose we have the function f(x) = x^2. If we apply a vertical stretch with a = 2, the transformed equation would be y = 2f(x) = 2(x^2).

Let’s compare the graphs of f(x) = x^2 and g(x) = 2x^2:

f(x) = x^2 g(x) = 2x^2
—————————————–
| |
| ** |
| * * |
| * * |
| * * |
| * * |
—————————————-
x-axis x-axis

In the above graph, the function f(x) = x^2 (represented with asterisks) is stretched vertically to form g(x) = 2x^2 (represented with stars). The stretching effect occurs because each y-coordinate is multiplied by 2.

So, whenever a is greater than 1, the function is vertically stretched. The magnitude of the stretch depends on the value of a.

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