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

  • Thread starter wScott
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In summary, when finding f(2x), you need to substitute 2x for the original x value. This will result in the graph being squeezed horizontally but not changed vertically. Another way to approach this is to substitute 2x for x in the original equation, which will give you (2x)^2 as the new function.
  • #1
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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  • #2
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?
 
  • #3
it becomes f(2x) = (2x)^2
 
  • #4
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.
 

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

What does the graph of f(2x) with a simple f(x) equation look like?

The graph of f(2x) with a simple f(x) equation will have the same shape as the graph of f(x), but it will be compressed horizontally by a factor of 2. This means that every point on the original graph will be half the distance from the y-axis on the new graph.

How do you graph f(2x) with a simple f(x) equation?

To graph f(2x), you can first create a table of values by plugging in different values for x into the original f(x) equation. Then, divide each x-value by 2 and plug the results into the f(2x) equation to get the corresponding y-values. Finally, plot the points on the graph and connect them to create the graph of f(2x).

How do you find the x-intercepts of the graph of f(2x) with a simple f(x) equation?

The x-intercepts of the graph of f(2x) will be the same as the x-intercepts of the original f(x) graph. To find them, set the y-value in the f(x) equation to 0 and solve for x. Then, divide the resulting x-values by 2 to get the x-intercepts of the f(2x) graph.

How do you find the y-intercept of the graph of f(2x) with a simple f(x) equation?

The y-intercept of the graph of f(2x) will also be the same as the y-intercept of the original f(x) graph. To find it, set the x-value in the f(x) equation to 0 and solve for y. Then, plug the resulting y-value into the f(2x) equation to get the y-intercept of the f(2x) graph.

What is the relationship between the slopes of the graphs of f(2x) and f(x)?

The slope of the graph of f(2x) will be 2 times steeper than the slope of the graph of f(x). This means that if the slope of f(x) is positive, the slope of f(2x) will be positive and twice as steep, and if the slope of f(x) is negative, the slope of f(2x) will be negative and twice as steep.

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