document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=15120>Question 15120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the DOMAIN and RANGE for the following equations:<BR>\n" );
document.write( "1)  y = 3x - 4<BR>\n" );
document.write( "2)  y = -2x^2 + 2<BR>\n" );
document.write( "3)  y = x^3\r<BR>\n" );
document.write( "\n" );
document.write( "I know how to graph I understand all that but I don'T know how to determine the range and domain, are they looking for number pairs????\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #7523 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=7523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in these equations or functions as we call them you know that x is called the independent variable and y the dependent variable. that is we give different values to x and find the corresponding values of y.that is how you draw the graphs of the functions .<BR>\n" );
document.write( "  now to start with domain is the set of all values x can take and range is the corresponding set of values y can take .<BR>\n" );
document.write( "  what do we mean by the set of values x can take .As you know certain operations are prohibited or meaning less in maths.like division by zero.so if we have a function y=1/x , we say x can take any value except zero.so domain of x is all real numbers except zero . similarly if y= square root of x ,then domain is ... x can take all real non negative numbers.x cannot be negative as square root of negative number does not exist.<BR>\n" );
document.write( "  after determining the domain ,we find the set of corresponding values of y and call it the range of y.clear ?<BR>\n" );
document.write( "  now y=3*x-4 .. as there are no problem areas like division by x or squareroot of x etc..we can conclude that domain of x is all real numbers and range of y is also all real numbers<BR>\n" );
document.write( " now   y = -2x^2 + 2...domain of x is all real numbers as above.but as far as range is concerned we see that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%2A%281-x%5E2%29 ALIGN=MIDDLE  ALT=\"y=2%2A%281-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...since square of x is always positive,its minimum value can be 0.hence -(square of x) has a maximum value of 0.hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-x%5E2 ALIGN=MIDDLE  ALT=\"1-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a maximum value of 1. hence y has a maximum value of 2 . hence range of y is all real numbers less than or equal to  2.you can check this from your graph too. you will find that as x changes from -infinity to +infinity , y changes from +2 to -infinity.<BR>\n" );
document.write( " <BR>\n" );
document.write( " y = x^3...you can see here domain and range are set of all real numbers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "   \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );