document.write( "Question 876612: Find the domain and range for the following function:
\n" ); document.write( "f(x)= 9x^3+4x^2-7\r
\n" ); document.write( "\n" ); document.write( "I have tried looking up how to do these and also in my math book, but it does not give good examples.... Please help!! \n" ); document.write( "
Algebra.Com's Answer #528878 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "f(x)= 9x³+4x²-7\r\n" );
document.write( "\r\n" );
document.write( "The DOMAIN is the set of all numbers on the x-axis, such that if\r\n" );
document.write( "you were to draw a VERTICAL line through it in both directions up\r\n" );
document.write( "and down long enough it would intersect the curve.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The RANGE is the set of all numbers on the y-axis, such that if\r\n" );
document.write( "you were to draw a HORIZONTAL line through it in both directions right\r\n" );
document.write( "and left long enough it would intersect the curve.\r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-10%2C10%2C-10000%2C10000%2C9x%5E3%2B4x%5E2-7%29\"\r\n" );
document.write( "\r\n" );
document.write( "-------------------\r\n" );
document.write( "\r\n" );
document.write( "Notice \r\n" );
document.write( "\r\n" );
document.write( "1. That the graph is such that if you were to draw a VERTICAL line through \r\n" );
document.write( "any point on the x-axis in both directions long enough it would intersect the\r\n" );
document.write( "curve.\r\n" );
document.write( "\r\n" );
document.write( "2. That the graph is such that if you were to draw a HORIZONTAL line through \r\n" );
document.write( "any point on the y-axis in both directions long enough it would intersect the\r\n" );
document.write( "curve.\r\n" );
document.write( "\r\n" );
document.write( "That's why both the domain and the range of f(x) are (-infinity,infinity)\r\n" );
document.write( "\r\n" );
document.write( "-------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "Another way to look at it is:\r\n" );
document.write( "\r\n" );
document.write( "The DOMAIN of y = 9x³+4x²-7 consists of all the numbers you can substitute \r\n" );
document.write( "for x and get a value for y.  The expression 9x³+4x²-7 contains no\r\n" );
document.write( "denominators that could ever be 0 and there are no square roots that\r\n" );
document.write( "could have negative numbers under them.  \r\n" );
document.write( "\r\n" );
document.write( "Therefore there are no restrictions on what numbers you can substitute for\r\n" );
document.write( "x and get a value for y.\r\n" );
document.write( "\r\n" );
document.write( "So the domain is \"ALL REAL NUMBERS\" or (-infinity, infinity) \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The RANGE of y = 9x³+4x²-7 consists of all the numbers you can GET \r\n" );
document.write( "for y by substituting value for x.  The expression 9x³+4x²-7 contains no\r\n" );
document.write( "denominators that could ever be 0 and there are no square roots that\r\n" );
document.write( "could have negative numbers under them.  \r\n" );
document.write( "\r\n" );
document.write( "\"graph%28400%2C400%2C-10%2C10%2C-10000%2C10000%2C9x%5E3%2B4x%5E2-7%29\" \r\n" );
document.write( "\r\n" );
document.write( "Notice that it goes infinitely low on the left and infinitely high on the\r\n" );
document.write( "right.  And there are no gaps in the curve anywhere.\r\n" );
document.write( "\r\n" );
document.write( "So the RANGE is also \"ALL REAL NUMBERS\" or (-infinity, infinity)  \r\n" );
document.write( "\r\n" );
document.write( "----------------------------\r\n" );
document.write( "\r\n" );
document.write( "The DOMAIN for every ODD-DEGREE polynomial function is (-infinity, infinity).\r\n" );
document.write( "\r\n" );
document.write( "The RANGE for every ODD-DEGREE polynomial function is (-infinity, infinity).\r\n" );
document.write( "\r\n" );
document.write( "The DOMAIN for every EVEN-DEGREE polynomial function is (-infinity, infinity).\r\n" );
document.write( "\r\n" );
document.write( "However the RANGE for an EVEN-DEGREE polynomial is NOT (-infinity, infinity).\r\n" );
document.write( "\r\n" );
document.write( "The range of an EVEN-DEGREE polynomial is either:\r\n" );
document.write( "\r\n" );
document.write( "(-infinity, MAXIMUM VALUE OF y) or  (MINIMUM VALUE OF y, infinity).\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );