Question

What is the effect on the graph of the function f(x)=2^x when f(x) is replaced with f(-1/2x)

Answer 1

Transformed function f(-1/2x), reflects over y-axis and a horizontal stretch by a factor of 1/2.

Explanation:

We are given parent function f(x) = 2^x.

And transformed function f(-1/2x).

According to rule of transformations, y= f(-x) reflects over y-axis and

y= f(bx) is horizontal stretch if b is greater than 0 and less than 1.

Therefore,

Transformed function f(-1/2x), reflects over y-axis and a horizontal stretch by a factor of 1/2.

Answer 2

It makes the graph much flatter. And it will flip it.

The graph will always have a point of (0, 1) and while both grow exponentially, the second graph will be slowed. For instance, the point x = 2 on the first graph will yield 4. Whereas in order to get 4 on the next graph, you would have to get all the way to -4.