Question 1204975
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Answer: <font color=red size=4>(-4, 5)</font>
This represents the interval -4 < x < 5


Explanation


Going from f(x) to f(x+2) will shift the curve 2 units to the left.
The decreasing interval will also shift this amount.
Subtract 2 from each endpoint
-2 becomes -2-2 = -4
7 becomes 7-2 = 5
The decreasing interval for y = f(x+2) is <font color=red>(-4, 5)</font> which is interval notation for -4 < x < 5.


If you are wondering "why does the x+2 mean shift 2 units left instead of 2 units right?" the reason is that the replacement of x with x+2 will move the xy axis 2 units to the right. 
Holding the curve in place gives the illusion it moves 2 units left.
Take a look at the graph of y = x^2 and y = (x+2)^2 for instance.
Desmos and GeoGebra are two graphing tools I recommend.


What's an example of a function that decreases on the interval -2 < x < 7?
There are infinitely many possible, but one example is f(x) = (200/243)(x-2.5)^3 - 50x
Replace every x with x+2 to end up with g(x) = (200/243)(x+2-2.5)^3 - 50(x+2) to find the decreasing interval has shifted 2 units leftward.
Desmos graph link
<a href="https://www.desmos.com/calculator/49glyjmlkw">https://www.desmos.com/calculator/49glyjmlkw</a>


If you were to type <font color=green>decreasing (200/243)(x-2.5)^3 - 50x</font> into WolframAlpha, then it will tell you that the decreasing interval is -2 < x < 7, and also highlight the decreasing portion.
<a href="https://www.wolframalpha.com/input?i=decreasing+%28200%2F243%29%28x-2.5%29%5E3+-+50x">https://www.wolframalpha.com/input?i=decreasing+%28200%2F243%29%28x-2.5%29%5E3+-+50x</a>
Then type in <font color=green>decreasing (200/243)(x+2-2.5)^3 - 50(x+2)</font> to see how the interval shifts.
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