Question

How does g(x) = 2(x-3)^3 change from x^3?

Im not sure about vertical/horizontal compressions/stretches.. Explanation of it as an extra would be appreciated :) How does g(x) = 2(x-3)^3 change from x^3?

Im not sure about vertical/horizontal compressions/stretches.. Explanation of it as an extra would be appreciated :) @Mathematics

Answer 1

The parent function is the second one that you wrote. Note the change that is with x, x-3. That affects the domain values, and means that the graph is shifted to the right 3 units. A horizontal shift.
The coefficient in front of the cubic, 2, means that the range (y-values) is stretched by a factor of 2. A vertical stretch is the result.
I hope this helps. Let me know if you need more explanation!

Answer 2

I understood the horizontal shift by 3 units, but I'm confused with whawt the difference of vertical stretch and compression.
Stretch is 2 and compression is 1/2, but sometimes they work the other way, etc..

Answer 3

A vertical stretch is defined like this: \[f \left( x \right)\rightarrow af \left( x \right)\],
where if the number "a" is greater than 1, it stretches the range by that multiplier, a. If the number "a" is less than one, but greater than zero, then it "flattens" the range, compressing it.

Answer 4

So for example, f(x) = 1/2x^3 with a parent function of x^3 would have a vertical compression of 2, and 4x^3 would have a vertical stretch of 4?