# Transformation of a graph

1. Oct 21, 2006

### bjgawp

[/PLAIN] [Broken]

For this graph, I'm not sure exactly how the equation y = (x³+1)² is transformed to get the graph (x³/8 + 1)². I said that it was just horizontally stretched by a factor of 8 but there has been a change in its intercepts. Also, not all the x-coordinates are changed by a factor of 8. Can anyone help clarify this for me? Thanks in advance

Last edited by a moderator: Apr 22, 2017 at 1:33 PM
2. Oct 21, 2006

### 0rthodontist

Compare $$(x^3 + 1)^2$$
to $$(\frac{x^3}{8} + 1)^2$$
The latter equals
$$((\frac{x}{2})^3 + 1)^2$$
Now let's say that I plug in a value x1 to f(x) for some function f, and get a value y1 back. Now what number x2 should I plug into the function g(x) = f(x/2) to get the same value y1? This is asking, what should x2 be if you have f(x1) = f(x2 / 2)? Do you see how to apply this to your problem?

3. Oct 21, 2006

### bjgawp

Oh .. so it isn't horizontally stretched by a factor of 8 but rather a factor of 2? It seems to work out that way:

f(x) - (1,4), (-1,0) ...
g(x) - (2,4), (-2,0) ...

Hmm... can someone explain why is it so? At a first glance, one would assume that the 1/8 would affect the original graph rather than 1/2

4. Oct 21, 2006

### 0rthodontist

:grumpy: :grumpy:

5. Oct 22, 2006

### HallsofIvy

Staff Emeritus
As was just pointed out to you, g(x) = f(x/2). x itself is not divided by
8. That should be all the expanation you need.