The cubing Function

Question

The graph of the parent function f(x)=x³ is transformed such that g(x)=f(-2x). How does the graph of g(x) compare to the graph of f(x)

Answer 1

First, plot the basic function. For positive x, you will get a curve rising steeply in the 1st quadrant (+x, +y). For negative x, it will be a mirror image in the 3rd quadrant (-x, -y)

To solve the new function, simply substitute the expression -2x for the x in the original.

Now we have y = (-2x)³

This has 2 effects:

The curve becomes steeper

The curve is flipped around the y axis---+x values now give negative y, and -x now gives +y

Plot a few points to see this....