Question 966077: I need help with the following problem:
If point P is on the graph of a function 'F', find the corresponding point on the graph of the given function:
P(0,5); y=f(x+2)-1
Thank you
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f(x+2) - 1 shifts the graph to the left 2 units and down 1 unit.
the point (0,5) on the grpah of f(x) becomes the point (-2,4) on the graph of f(x+2) - 1.
if we let the graph of f(x) be equal to x + 5, this is what it looks like:
the graph of f(x) is equal to x + 5.
when x = 0, y = 5.
that's the black line on the grpah.
f(x+2) shifts the graph to the left 2 units.
in the picture, the graph of f(x+2) is equal to (x+2) + 5.
that's the blue line on the graph.
you can see that the blue line had y = 5 when x = -2.
f(x+2) results in the identical graph shifted to the left 2 units on the x-axis.
f(x+2) - 1 is equal to (x+2) + 5 - 1.
that's the red line on the graph.
that's the same graph as f(x) except it's shifted to the left 2 units and then down 1 unit.
it's also the same graph as f(x+2) except it's shifted down 1 unit.
the corresponding point of (0,5) on the graph of f(x) is equal to (-2,4) on the graph of f(x+2) - 1.
that's your solution.
if you have trouble with the colors, the black line is on the bottom and the red line is in the middle and the blue line is on top.
the black line is f(x).
f(x) is equal to x + 5.
the blue line is f(x+2)
f(x+2) is equal to (x+2) + 5
the red line is f(x+2) - 1
f(x+2) - 1 is equal to (x+2) + 5 - 1
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