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:
- Stretch f(x) vertically by a scale factor of 2
- Reflect the resulting function across the x-axis.
Assume the resulting function is: g(x)
This means that:
[tex]g(x) = -2f(x)[/tex]
First, f(x) has to be stretched vertically by a scale factor of 2.
The rule of this transformation is:
[tex](x,y) \to (x,by)[/tex]
Where:
[tex]b =2[/tex] --- the scale factor.
So, after the first transformation, the function is:
[tex]f'(x) =2f(x)[/tex]
Next, reflect f'(x) across the x-axis.
The rule of this transformation is:
[tex](x,y) \to (x,-y)[/tex]
This means that:
[tex]g(x) = -f'(x)[/tex]
Substitute: [tex]f'(x) =2f(x)[/tex]
[tex]g(x) = 2f(x)[/tex]
Hence, the transformations are:
- Stretch f(x) vertically by a scale factor of 2
- Reflect the resulting function across the x-axis.
Read more about transformations at:
brainly.com/question/24326503
