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Question 276409: If the graph of f is decreasin on [0,infinity)the what can be said about the graph of y=f(-x)+1? The graph of y=-f(x)-1?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If the graph of f is decreasing on [0,infinity)the what can be said about the graph of y=f(-x)+1? The graph of y=-f(x)-1?
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f(-x) + 1 is a reflection in the y-axis and a +1 vertical shift.
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If f(x) is decreasing to the right of the y-axis
f(-x) will be increasing to the left of the y-axis.
The +1 will move all points 1 unit up but the function
will still be increasing on (-infinity,0]
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-f(x)-1 is a reflection in the x-axis followed by a vertical shift down one
If f(x) is decreasing to the right of the y-axis
-f(x) will be increasing to the right of the y-axis.
The -1 will move all points 1 unit down but the function
will still be increasing on [0,+infinity)
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Cheers,
Stan H.
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