Question

Consider the function F(x) = 2f(x) = 2(2^x). What transformation does the function F(x) = 2f(x) represent?

a) Horizontal compression by a factor of 2
b) Vertical stretch by a factor of 2
c) Reflection about the x-axis
d) Translation to the left by a factor of 2 units

Answer 1

The function F(x) = 2f(x) represents a vertical stretch by a factor of 2, where the height of the graph is doubled for each x-value.

Step-by-step explanation:

The transformation represented by the function F(x) = 2f(x) = 2(2^x) is a vertical stretch by a factor of 2. This type of transformation takes the original function f(x) and stretches its graph vertically, meaning the y-values of the function are multiplied by 2, resulting in all points on the graph moving twice as far from the x-axis. Therefore, for every x-value, the height of the function's graph increases by a factor of two.