I know that certain equation cause a transformation (ie, y=f(x-2)) and I wasn't sure how absolute values affect the original function. I'm given y=f(x), which is a curve with points at (-2,1), (-1, .75), (0,0), (1, 1), and (2,0).
Also, how do the effects differ between f(|x|) and |f(x)|?
Thanks in advance!
Also, how do the effects differ between f(|x|) and |f(x)|?
Thanks in advance!
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For the graph of y=f(|x|), erase the left hand side of the graph (the part where x is negative).
Draw in a mirror image of the right hand side of the graph, ie. reflect the graph from the positive values of x across the y-axis.
(-2, 0) (-1, 1) (0,0) (1,1) (2,0)
Regarding the graph of |f(x)|, that's different. This time erase the bottom half of the graph (the part where y is negative) and draw in a mirror image of the top half of the graph, ie. reflect the graph from the positive values of y across the x-axis.
(-2, 1) (-1, .75) (0,0) (1,1) (2,0)
I hope this helps.
Draw in a mirror image of the right hand side of the graph, ie. reflect the graph from the positive values of x across the y-axis.
(-2, 0) (-1, 1) (0,0) (1,1) (2,0)
Regarding the graph of |f(x)|, that's different. This time erase the bottom half of the graph (the part where y is negative) and draw in a mirror image of the top half of the graph, ie. reflect the graph from the positive values of y across the x-axis.
(-2, 1) (-1, .75) (0,0) (1,1) (2,0)
I hope this helps.
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f(|x|) would be (-2, 0), (-1, 1), (0, 0), (1, 1), and (2, 0). The points to the left of the y-axis are reflections of the points to the right, over the y-axis.
|f(x)| would be (-2, 1), (-1, 0.75), (0, 0), (1, 1), and (2, 0). The points below the x-axis are reflected above the x-axis.
|f(x)| would be (-2, 1), (-1, 0.75), (0, 0), (1, 1), and (2, 0). The points below the x-axis are reflected above the x-axis.
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if you have a negative x value, the absolute value symbol would make the x value positive.
so it would be (2,1) (1, .75) (0,0) and (1,1)
(absolute value = the distance from 0)
so it would be (2,1) (1, .75) (0,0) and (1,1)
(absolute value = the distance from 0)
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the -x and +x sides are exact mirror images of each other
just plot y = f(x), x>0
and for the -ve part ie x < 0, draw the mirror image of x > 0
just plot y = f(x), x>0
and for the -ve part ie x < 0, draw the mirror image of x > 0