Understanding the Transformation of a Graph - Can You Help Clarify?

In summary, the conversation discusses the transformation of the equation y = (x³+1)² to (x³/8 + 1)² and how it affects the graph. After some discussion, it is determined that the transformation is not a horizontal stretch by a factor of 8, but rather a factor of 2 due to the function g(x) = f(x/2). This explains the change in intercepts and x-coordinates. There is also a question regarding how to find the value of x2 in g(x) if f(x1) = f(x2/2).
  • #1
bjgawp
84
0
http://img147.imageshack.us/img147/6277/1fox7.jpg [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
 
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  • #2
Compare [tex](x^3 + 1)^2[/tex]
to [tex](\frac{x^3}{8} + 1)^2[/tex]
The latter equals
[tex]((\frac{x}{2})^3 + 1)^2[/tex]
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
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
bjgawp said:
Hmm... can someone explain why is it so?
:grumpy: :grumpy:
 
  • #5
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.
 

1. What is the transformation of a graph?

The transformation of a graph refers to the changes made to the original graph, such as shifting, stretching, compressing, or reflecting, to create a new graph with altered attributes.

2. Why do we need to transform a graph?

Transforming a graph allows us to visually represent changes in data or equations, making it easier to interpret and understand the information being presented.

3. What are the common types of transformations in a graph?

The most common types of transformations in a graph include translation (shifting), dilation (stretching or compressing), and reflection (flipping).

4. How do you determine the direction of a graph transformation?

The direction of a graph transformation can be determined by looking at the changes made to the equation or data. For example, if the equation is shifted to the right, the graph will also shift to the right.

5. Can a graph be transformed in more than one way?

Yes, a graph can be transformed in more than one way. For example, a graph can be shifted up and to the right, creating a new position and shape for the graph.

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