document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016793>Question 1016793</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ¿Necesito ayuda con descubrir lo que significa un círculo abierto y un qué círculo cerrado significa en un gráfico del dominio y del rango? AHORA. No juegue conmigo.<BR>\n" );
document.write( " </SPAN>\n" );
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document.write( "Usualmente un círculo cerrado significa que ese valor de la variable es parte del domino o del rango de la función,<BR>\n" );
document.write( "y un círculo abierto significa que ese valor de la variable no es parte del domino o del rango de la función.<BR>\n" );
document.write( "Por ejemplo, el domino de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > es todos los números reales excepto el <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > . En ese caso <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.9 ALIGN=MIDDLE  ALT=\"2.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.99 ALIGN=MIDDLE  ALT=\"2.99\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.999 ALIGN=MIDDLE  ALT=\"2.999\"   DISABLED_style= \"max-width:90%; height:auto;\" > , etcétera, son parte del dominio, de la función, pero <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > no lo es. Hay differentes formas de expresar el dominio y/o rango de una función. Puede ser que tu clase esté practicando como hacerlo gráficamente. En ese caso, el dominio de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > se graficaría como una linea numérica con un \"agujero\" en el valor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "El ancho/diámetro de ese agujero es infinitamente chico, pero lo dibujamos como un circulo con la parte de adento vacía:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C100%2C-0.5%2C5.5%2C-0.5%2C0.5%2C%0D%0Aarrow%282.9%2C0%2C5.5%2C0%29%2Carrow%282%2C0%2C-0.5%2C0%29%2C%0D%0Ared%28line%28-0.5%2C0%2C2.95%2C0%29%29%2Cred%28line%283.05%2C0%2C5.5%2C0%29%29%2C%0D%0Ared%28circle%283%2C0%2C0.05%29%29%2C%0D%0Aline%280%2C0%2C0%2C-0.1%29%2Clocate%28-0.05%2C-0.1%2C0%29%2C%0D%0Aline%281%2C0%2C1%2C-0.1%29%2Clocate%280.95%2C-0.1%2C1%29%2C%0D%0Aline%282%2C0%2C2%2C-0.1%29%2Clocate%281.95%2C-0.1%2C2%29%2C%0D%0Aline%283%2C0%2C3%2C-0.1%29%2Clocate%282.95%2C-0.1%2C3%29%2C%0D%0Aline%284%2C0%2C4%2C-0.1%29%2Clocate%283.95%2C-0.1%2C4%29%2C%0D%0Aline%285%2C0%2C5%2C-0.1%29%2Clocate%284.95%2C-0.1%2C5%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "El dominio de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=sqrt%286%2Bx-x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=sqrt%286%2Bx-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > es el intervalo cerrado [-2,3], y lo representamos con circulos llenos en <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > y <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C100%2C-2.5%2C3.5%2C-0.5%2C0.5%2C%0D%0Aarrow%282%2C0%2C3.5%2C0%29%2Carrow%28-1%2C0%2C-2.5%2C0%29%2C%0D%0Ared%28line%28-1.95%2C0%2C2.95%2C0%29%29%2C%0D%0Ared%28circle%28-2%2C0%2C0.05%29%29%2Cred%28circle%28-2%2C0%2C0.04%29%29%2C%0D%0Ared%28circle%28-2%2C0%2C0.03%29%29%2Cred%28circle%28-2%2C0%2C0.02%29%29%2C%0D%0Ared%28circle%283%2C0%2C0.05%29%29%2Cred%28circle%283%2C0%2C0.04%29%29%2C%0D%0Ared%28circle%283%2C0%2C0.03%29%29%2Cred%28circle%283%2C0%2C0.02%29%29%2C%0D%0Aline%280%2C0%2C0%2C-0.1%29%2Clocate%28-0.05%2C-0.1%2C0%29%2C%0D%0Aline%281%2C0%2C1%2C-0.1%29%2Clocate%280.95%2C-0.1%2C1%29%2C%0D%0Aline%282%2C0%2C2%2C-0.1%29%2Clocate%281.95%2C-0.1%2C2%29%2C%0D%0Aline%283%2C0%2C3%2C-0.1%29%2Clocate%282.95%2C-0.1%2C3%29%2C%0D%0Aline%28-2%2C0%2C-2%2C-0.1%29%2Clocate%28-2.05%2C-0.1%2C-2%29%2C%0D%0Aline%28-1%2C0%2C-1%2C-0.1%29%2Clocate%28-1.05%2C-0.1%2C-1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "El dominio de <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=1%2Fsqrt%286%2Bx-x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=1%2Fsqrt%286%2Bx-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > es el intervalo abierto (-2,3), y lo representamos con circulos vacíos en <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > y <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C100%2C-2.5%2C3.5%2C-0.5%2C0.5%2C%0D%0Aarrow%282%2C0%2C3.5%2C0%29%2Carrow%28-1%2C0%2C-2.5%2C0%29%2C%0D%0Ared%28line%28-1.95%2C0%2C2.95%2C0%29%29%2C%0D%0Ared%28circle%28-2%2C0%2C0.05%29%29%2C%0D%0Ared%28circle%283%2C0%2C0.05%29%29%2C%0D%0Aline%280%2C0%2C0%2C-0.1%29%2Clocate%28-0.05%2C-0.1%2C0%29%2C%0D%0Aline%281%2C0%2C1%2C-0.1%29%2Clocate%280.95%2C-0.1%2C1%29%2C%0D%0Aline%282%2C0%2C2%2C-0.1%29%2Clocate%281.95%2C-0.1%2C2%29%2C%0D%0Aline%283%2C0%2C3%2C-0.1%29%2Clocate%282.95%2C-0.1%2C3%29%2C%0D%0Aline%28-2%2C0%2C-2%2C-0.1%29%2Clocate%28-2.05%2C-0.1%2C-2%29%2C%0D%0Aline%28-1%2C0%2C-1%2C-0.1%29%2Clocate%28-1.05%2C-0.1%2C-1%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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