document.write( "Question 1055224: If the range of g(x) = x^2+4 is all real numbers from 20 to 53, what negative numbers are in the domain of g(x) ? Use interval notation to express your answer. \n" ); document.write( "
Algebra.Com's Answer #670460 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "First we draw the graph of y = g(x) = x2+4\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "Then we draw horizontal lines at y=20 and at y=53, and indicate\r\n" );
document.write( "(in green on the y-axis) the given range.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then we find the points of intersection of the\r\n" );
document.write( "two horizontal lines and g(x), by solving these\r\n" );
document.write( "two systems:\r\n" );
document.write( "\r\n" );
document.write( "\"system%28y=x%5E2%2B4%2Cy=20%29\" and \"system%28y=x%5E2%2B4%2Cy=53%29\"\r\n" );
document.write( "\r\n" );
document.write( "by substitution and factoring:\r\n" );
document.write( "\r\n" );
document.write( "The points of intersection are (-7,53), (-4,20), (4,20), (7,53)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since the range is \"matrix%281%2C5%2C%22%7B%22%2Cy%2C%22%7C%22%2C20%3C=y%3C=53%2C%22%7D%22%29\",\r\n" );
document.write( "\r\n" );
document.write( "we erase the bottom of the graph that drops below y=20,\r\n" );
document.write( "and also the top of the graph that rises above y=53, for\r\n" );
document.write( "they are not part of g(x) with the given range:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now to find the domain, we draw lines from the endpoints\r\n" );
document.write( "of the graph down to the x-axis, shown below, and indicate \r\n" );
document.write( "(in green on the x-axis) the entire domain of g(x) \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The interval for the entire domain (in green on the x-axis) is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "However, the question only asks for the NEGATIVE part of the\r\n" );
document.write( "domain, so we only answer the left part of it, which is just\r\n" );
document.write( "this left part of the interval notation where x is negative:\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%281%2C5%2C%22%5B%22%2C-7%2C%22%2C%22%2C-4%2C%22%5D%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );