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Question 1204993: If (-1,-4) is a point on the graph of y=f(x), what point do you know is on the graph of y=f(1/2x)?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
I'm assuming the 1/2x should be (1/2)x.
I'll rewrite that as x/2.
g(x) = f(x/2)
The question is: what can we plug into g(x) to land on the known value f(x) = -4?
If we tried x = -1, then we'll get
g(x) = f(x/2)
g(-1) = f(-1/2)
That's no good because we don't know what f(-1/2) is.
But what if we tried x = -2
g(x) = f(x/2)
g(-2) = f(-2/2)
g(-2) = f(-1)
g(-2) = -4
So as you can see, the idea is to set the x/2 equal to the previous x value -1. Solving x/2 = -1 for x gets us the new input x = -2.
Since g(-2) = -4, we know that (-2,-4) is on g(x).
An example:
f(x) = 4x in green
g(x) = f(x/2) = 4(x/2) = 2x in blue
Use a graphing tool like GeoGebra or Desmos to try out other examples.
Replacing each input x with x/2 horizontally stretches the graph by a factor of 2.
Function g(x) is twice as wide, so to speak, compared to f(x).
Answer: (-2, -4)
Answer by ikleyn(52803)  (Show Source):
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