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.

hello from mrbilldoesmath!

answer:   x^2 + y^2 = 1024

discussion:

the equation of a circle with center (h,k) and radius "r" is

(x-h)^2 + (y-k)^2 = r^2.

in our case

(x-0)^2 + (y-0) ^2 = 32^2 = 1024

you,

mrb