document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204975>Question 1204975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> suppose the function y=f(x) is decreasing on the interval (-2,7). Over what interval is the graph of y=f(x+2) decreasing? </SPAN>\n" );
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document.write( "Answer: <font color=red size=4>(-4, 5)</font><BR>\n" );
document.write( "This represents the interval -4 < x < 5\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "Going from f(x) to f(x+2) will shift the curve 2 units to the left.<BR>\n" );
document.write( "The decreasing interval will also shift this amount.<BR>\n" );
document.write( "Subtract 2 from each endpoint<BR>\n" );
document.write( "-2 becomes -2-2 = -4<BR>\n" );
document.write( "7 becomes 7-2 = 5<BR>\n" );
document.write( "The decreasing interval for y = f(x+2) is <font color=red>(-4, 5)</font> which is interval notation for -4 < x < 5.\r<BR>\n" );
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document.write( "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. <BR>\n" );
document.write( "Holding the curve in place gives the illusion it moves 2 units left.<BR>\n" );
document.write( "Take a look at the graph of y = x^2 and y = (x+2)^2 for instance.<BR>\n" );
document.write( "Desmos and GeoGebra are two graphing tools I recommend.\r<BR>\n" );
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document.write( "What's an example of a function that decreases on the interval -2 < x < 7?<BR>\n" );
document.write( "There are infinitely many possible, but one example is f(x) = (200/243)(x-2.5)^3 - 50x<BR>\n" );
document.write( "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.<BR>\n" );
document.write( "Desmos graph link<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.desmos.com/calculator/49glyjmlkw\">https://www.desmos.com/calculator/49glyjmlkw</a>\r<BR>\n" );
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document.write( "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.<BR>\n" );
document.write( "<a  rel=nofollow 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><BR>\n" );
document.write( "Then type in <font color=green>decreasing (200/243)(x+2-2.5)^3 - 50(x+2)</font> to see how the interval shifts.<BR>\n" );
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