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Question 73027: When it says 'vertically stretch by a factor of.. , or vertically compress by a factor of.. , 'horizontally stretch by a factor of.. , or horizontally compress by a factor of.. ' is there some sort of calculation to use this factor and find additional points on the graph? I'm in section 3.1, starting with problem number 19. I understand the transformation processes of graphing these equations, I'm mainly looking for a way to know how to use that 'stretch/compress' factor to find additional points on the graph. Thank you for your help.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Let's say you start with the graph of a parabola: y=x^2
This is a statement regarding "y"; it is always "the square of x".
Now, look at y=3x^2
All those y-values are multiplied by 3; this "stretches" the curve so
it goes upward faster: the parabola will look narrower because it rises so fast.
Now look at y=(1/2)x^2
All those original y-values are multiplid by (1/2); this "compresses" the
curve so it looks flatter.
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There is no horizontal stretching or compressing but there is "shifting".
If you start with y=x^2 the vertex will occur at x=0
Replace "x" by "x+3" and the vertex will occur earlier on the x-axis; it will shift three to the left.
Replace "x" by "x-3" and the vertex will occur later on the x-axis; it will
shift three to the right.
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These are powerful tools for sketching curves. Learn how to use them and
you will save a lot of time you might otherwise use plotting points.
Cheers,
Stan H.
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