Question

If a function f(x) were to be stretched vertically by a factor that of 2 and compressed horizontally by a factor of 1/2 to make a new function g(x). Which transformation function would best describe this?

Answer 1

To transform the original function f(x) into the new function g(x) by vertical stretching and horizontal compression, the transformation function is g(x) = 2f(2x). This function doubles the output values and reduces the input values by half.

Step-by-step explanation:

If a function f(x) is vertically stretched by a factor of 2 and horizontally compressed by a factor of 1/2, it means that the new function g(x) is transformed in two ways. The vertical stretch by a factor of 2 can be represented by multiplying the function by 2, which means any output value of the function gets doubled. The horizontal compression by a factor of 1/2 means that the input to the original function must be multiplied by 2 for it to be equivalent to an input of 1 to the new function.

So the transformation that describes the new function g(x) is g(x) = 2f(2x). This transformation function not only doubles the value of the function at any point (vertical stretch) but also makes the function reach any point at half the input value it used to (horizontal compression).