# Transformation for y=2^0.5x

• October 8th 2012, 09:34 AM
ParieValle
Transformation for y=2^0.5x
Hello,
I've been given this question:
For the following equation, state the parent function and the transformation that was applied. Graph the transformed function.
I know that the parent function is y=2^x. But I don't understand how I would describe the transformation, and how I would graph it. If it was to the power of 0.5x how will it be different from just power to x?

• October 8th 2012, 10:47 AM
bjhopper
Re: Transformation for y=2^0.5x
For the transformed exponent find ordered pairs satisfying y= 2^.5x
Examples x=0 y=1, x=-4 y=1/4, x=4 y=4 continue and plot
• October 8th 2012, 11:27 AM
HallsofIvy
Re: Transformation for y=2^0.5x
Given the graph of y= f(x), any thing done before applying the function f is a change to x and affects the graph horizontally- because the x-axis is horizontal. Anything done after applying the function is a change to y and affects the graph vertically- because the y-axis is vertical.

Here, replacing x with 0.5x- that is, multiplying x by 1/2, stretches the graph horizontally. For example, the graph of $y= 2^x$ contains the points (0, 1) and (1, 2). The corrsponding points on the graph of $y= 2^{0.5x}= 2^{x/2}$ are (0, 1) and (2, 2). Same y values but the horizontal distace between them has doubled.