Justin O.

asked • 08/28/18

Assume (-2,3) is a point on the graph of f. What are the coordinates if y=-f(x/2)

Assume (-2,3) is a point on the graph of f. What are the coordinates if y=-f(x/2)

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Mark M. answered • 08/29/18

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Since (-2,3) is on the graph of y = f(x), f(-2) = 3.
 
So, if we let x = -4, then -f(x/2) = -f(-4/2) = -f(-2) = -3
 
If the point (-2,3) is on the graph of y = f(x), then the point (-4,-3) lies on the graph of y = -f(x/2).
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Mark M.

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Another way to look at the problem:
 
   Replacing x by x/2 stretches the graph of y = f(x) horizontally by a factor of 2.
 
   Negating f(x) reflects the graph in the x-axis. 
 
So, replacing x by x/2 translates (-2,3) to the point (-4,3).  Reflecting in the x-axis sends (-4,3) to (-4,-3).
 
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08/29/18

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