document.write( "Question 1209870: Fill in the blanks.\r
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\n" ); document.write( "\n" ); document.write( "If f(x) is an even function and g(x) is an even function and h(x) is an even function, then f(x) + g(x) + h(x) is an ___ function.\r
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\n" ); document.write( "\n" ); document.write( "If f(x) is an odd function and g(x) is an odd function and h(x) is an even function, then f(x)*g(x) + h(x) is an ___ function.\r
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\n" ); document.write( "\n" ); document.write( "If f(x) is an even function and g(x) is an odd function and h(x) is an odd function, then f(x)*(g(x) + h(x)) is an ___ function.\r
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\n" ); document.write( "\n" ); document.write( "If f(x) is an odd function and g(x) is an even function and h(x) is an odd function, then f(x)*g(x)*h(x) is an ___ function.
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Algebra.Com's Answer #850923 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "An even function is symmetrical with respect to the x axis,\r\n" );
document.write( "An odd function is symmetrical with respect to the origin.\r\n" );
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document.write( "Two examples of even functions are f(x) = x2 and g(x) = x4 \r\n" );
document.write( "\"graph%28100%2C100%2C-2%2C2%2C-2%2C2%2Cx%5E2%29\"   \"graph%28100%2C100%2C-2%2C2%2C-2%2C2%2Cx%5E4%29\"\r\n" );
document.write( "If you add two even functions, you get:\r\n" );
document.write( "\"graph%28100%2C100%2C-2%2C2%2C-2%2C2%2Cx%5E2%2Bx%5E4%29\", which is an even function. \r\n" );
document.write( "If you multiply two even functions, you get:\r\n" );
document.write( "\"graph%28100%2C100%2C-2%2C2%2C-2%2C2%2Cx%5E2%2Ax%5E4%29\", which is an even function. \r\n" );
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document.write( "Two examples of odd functions are h(x) = x3 and k(x) = x5 \r\n" );
document.write( "\"graph%28100%2C100%2C-2%2C2%2C-2%2C2%2Cx%5E3%29\"   \"graph%28100%2C100%2C-2%2C2%2C-2%2C2%2Cx%5E5%29\"\r\n" );
document.write( "If you add two odd functions, you get:\r\n" );
document.write( "\"graph%28100%2C100%2C-2%2C2%2C-2%2C2%2Cx%5E3%2Bx%5E5%29\", which is an odd function.\r\n" );
document.write( "If you multiply two odd functions, you get:\r\n" );
document.write( "\"graph%28100%2C100%2C-2%2C2%2C-2%2C2%2Cx%5E3%2Ax%5E5%29\", which is an even function.\r\n" );
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document.write( "An example of adding an even function to an odd function is adding \r\n" );
document.write( "f(x) = x2 and  h(x) = x3\r\n" );
document.write( "You get:\r\n" );
document.write( "\"graph%28100%2C100%2C-2%2C2%2C-2%2C2%2Cx%5E2%2Bx%5E3%29\" <---Watch out for this case!!\r\n" );
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document.write( "If you look close, that function is nether even nor odd. It is neither\r\n" );
document.write( "symmetrical with respect to the y axis nor the origin.\r\n" );
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document.write( "If you multiply an even function by an odd function, you get\r\n" );
document.write( "\"graph%28100%2C100%2C-2%2C2%2C-2%2C2%2Cx%5E2%2Ax%5E3%29\", which is an odd function,\r\n" );
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document.write( "Now you have all the information you need to answer the questions.\r\n" );
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document.write( "And, for godssake, don't trust Artificial Intelligence's solutions.  \r\n" );
document.write( "Sometimes he's right and sometimes he's wrong.  He is still learning.\r\n" );
document.write( "Someday he'll get them all right when he learns enough, but at the \r\n" );
document.write( "present, don't trust him!\r\n" );
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document.write( "Edwin
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