The area of the triangle formed by the graph of y=2f(2x) is 32⋅4= 128 .
The graph of y=2f(2x) is the result of applying the following transformations in turn to the graph of y=f(x):
A dilation by a factor of 2 in both the x and y directions.
A reflection across the y-axis.
The first transformation multiplies the area of the triangle by a factor of 2^2 =4.
The second transformation has no effect on the area. Therefore, the area of the triangle formed by the graph of y=2f(2x) is 32⋅4= 128 .
Question
Suppose the function $f(x)$ is defined on the domain $\{x_1,x_2,x_3\}$, so that the graph of $y=f(x)$ consists of just three points. Suppose those three points form a triangle of area $32$. The graph of $y = 2f(2x)$ also consists of just three points. What is the area of the triangle formed by those three points?