document.write( "Question 1039192: A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph.
\n" ); document.write( "f(x)= x^3; shift upward 4 units \n" ); document.write( "

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Shifting the graph upwards by $\"4\"$ units means that
\n" ); document.write( "for every value of $\"x\"$ , the point $\"P%28x%2Cy%29\"$ will shift to a point $\"Q%28x%2Cy%2B4%29\"$ with a value of $\"y\"$ that is $\"4\"$ more.
\n" ); document.write( "Instead of the point $\"P%28x%2Cf%28x%29%29\"$ in the original function graph,
\n" ); document.write( "the new graph will contain the point $\"Q%28x%2Cf%28x%29%2B4%29\"$ .
\n" ); document.write( "So, for any function $\"f%28x%29\"$ , the equation for the function corresponding to the a graph shiftedr up by $\"4\"$ is
\n" ); document.write( " $\"g%28x%29=f%28x%29%2B4\"$ .
\n" ); document.write( "In the case of $\"f%28x%29=x%5E3\"$ , the function for the shifted graph is
\n" ); document.write( " $\"g%28x%29=highlight%28x%5E3%2B4%29\"$ . \n" ); document.write( "

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