Graph f(2x) with a Simple f(x) Equation

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Homework Help Overview

The problem involves graphing the function f(2x) where the original function is f(x) = x^2. Participants are exploring how the transformation affects the graph of the function.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss substituting 2x into the original function and question whether the resulting values will double. There are attempts to clarify the transformation and its impact on the graph's shape and position.

Discussion Status

The discussion is active with various interpretations being explored. Some participants provide guidance on how to approach the substitution, while others emphasize the horizontal transformation of the graph. There is no explicit consensus yet on the best method to visualize the transformation.

Contextual Notes

Participants are working under the constraints of homework guidelines, which may limit the depth of their exploration. There is a focus on understanding the implications of the transformation rather than deriving a complete solution.

wScott
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Homework Statement


Given f(x) = x^2. Graph f(2x)

Homework Equations



I just need to draw the graph

The Attempt at a Solution



What I tried was putting the x value in the equation which would give me the y value by means of the x^2 part, and the x value would double to give me my new point. This wasn't what the answer key had. Any tips?
 
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When you are asked to find f(2x), you need to substitute 2x as a whole for the original x. Will the value of f(x) really double?
 
it becomes f(2x) = (2x)^2
 
There are two ways to do this. The simplest is to do what theperthvan (and, indirectly, Tedjn) suggests: replace x by 2x. What is (2x)2?

The other is to argue that any change before the "main" function, x2, is applied is a change in x and so changes the graph only horizontally. The value x= 1, after multiplying by 2, becomes the same as x= 2. But 1 is only 1/2 as far from the origin as 2: the whole graph of y= x2 is "squeezed" by 1/2 horizontally but not changed vertically.
 

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