What transformation of the parent function f(x) is made to get −2f(x)?

The transformation of a function involves changing the position and/or size of the original function to another. The transformation to give -2f(x) are:

Assume the resulting function is: g(x)

This means that:

First, f(x) has to be stretched vertically by a scale factor of 2.

The rule of this transformation is:

Where:

--- the scale factor.

So, after the first transformation, the function is:

Next, reflect f'(x) across the x-axis.

The rule of this transformation is:

This means that:

Substitute:

Hence, the transformations are:

Read more about transformations at:

link

1. Stretch the graph of the parent function vertically by a factor of 2.

2. Reflect the entire graph of your result across the x-axis.