document.write( "Question 957400: If k(x) is a function.What is the relationship between k(x) and k(-x) \n" ); document.write( "

Algebra.Com's Answer #585018 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
let take an example:\r
\n" ); document.write( "\n" ); document.write( " graph $\"k%28x%29+=+x%5E3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3%29+\"$ \r
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\n" ); document.write( "\n" ); document.write( "now, pay good attention what will happen if I put $\"-x\"$ in for $\"x\"$ :
\n" ); document.write( "
\n" ); document.write( " $\"k%28-x%29+=%28-x%29%5E3=+-x%5E3\"$ \r
\n" ); document.write( "\n" ); document.write( "see it on a graph:\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%5E3%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "This transformation rotated the original graph around the $\"y-axis\"$ . Any points on the $\"y-axis\"$ stay on the $\"y-axis\"$ ; it's the points off the axis that switch sides. This is always true: \r
\n" ); document.write( "\n" ); document.write( " $\"k%28-x%29\"$ is the $\"mirror\"$ $\"+image\"$ of $\"k%28x%29\"$ , as reflected in the y-axis. \r
\n" ); document.write( "\n" ); document.write( "see both on a graph:\r
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2Cx%5E3%2C+-x%5E3%29+\"$ \r
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