SOLUTION: Suppose that the function y=f(x) is decreasing on the interval (-2,7). Over what interval is the graph of y=f(x+2) decreasing? Explain step by step

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Question 1139699: Suppose that the function y=f(x) is decreasing on the interval (-2,7). Over what interval is the graph of y=f(x+2) decreasing? Explain step by step
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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The graph of the function y = f(x+2) is the graph of the parent function y = f(x) shifted 2 units to the left.


Therefore, if the graph of y = f(x) is decreasing on the interval (-2,7),

then we can state that the graph y = f(x+2) is decreasing on the interval (-4,5).


It is that step by step explanation you requested for.

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The major fact you should learn and memorize from my post is THIS :

    The graph of the function y = f(x+2) is the graph of the parent function y = f(x) shifted 2 units to the left.

If you know and understand it, you can easily solve any problem of this kind.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
if the function y=f%28x%29 is decreasing on the interval (-2,7)
over what interval is the graph of y=f%28x%2B2%29
find value of x such that
x%2B2+=+-2
x+=+-2-2
x+=+-4


x+%2B+2+=+7%0D%0A%0D%0A%7B%7B%7Bx+=+7-2
x=5

so, f%28x+%2B+2%29 decreasing over the interval (-4, 5)