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How do I transform this function by y=f(3x) if this is the original function?

How do I transform this function by y=f(3x) if this is the original function?-example-1
User Jianfeng
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1 Answer

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Let y=f(x) is the original function and y=f(ax) is the new function, where a is a constant.

Then, y=f(ax) is a horizontal stretch or horizontal compression of f(x).

If a>1, then the graph of f(x) is compressed by 1/a.

If 0

The given function is y=f(x).

The new function is y=f(3x). It is of the form y=f(ax).

The constant 3 is greater than 1.

Therefore, the graph of y=f(3x) is the compression of the graph of f(x) by 1/3.

Identify some points on the graph of f(x) in the form (x, y).

(3, 0), (0, 3) and (-3, 0 ) are points on the graph of f(x).

Let (x', y') be a point on the graph of y=f(3x).

The transformation of each of the point on y=f(x) to y=f(3x) can be represented as,

(x, y)-->(x', y')-->(x/3, y).

For points (3, 0), (0, 3) and (-3, 0 ), the transformation can be described by ,


\begin{gathered} (3,\text{ 0)}\longrightarrow(3,\text{ }3*0)=(3,\text{ 0)} \\ (0,\text{ 3)}\longrightarrow(0,\text{ 3}*3\text{)=}(0,\text{ 9)} \\ (-3,0)\longrightarrow(-3,3*0)=(-3,\text{ 0)} \end{gathered}

User Autonocat
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