document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=846913>Question 846913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The range of a function f(x) = 4x-5 is (-1, 7) find its domain<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #509963 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=509963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the functionm is:<BR>\n" );
document.write( "f(x) = 4x- 5<BR>\n" );
document.write( "the range is  (-1,7)<BR>\n" );
document.write( "this means that -1 < x < 7\r<BR>\n" );
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document.write( "replace f(x) with those values to see what the corresponding value of x is.\r<BR>\n" );
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document.write( "-1 = 4x - 5 is your first equation.<BR>\n" );
document.write( "add 5 to both sides to get 4 = 4x<BR>\n" );
document.write( "divide both sides by 4 to get x = 1.<BR>\n" );
document.write( "when x = 1, 4x - 5= -1<BR>\n" );
document.write( "x can't be equal to 1, because then f(x) would be equal to 1 and that's not in the range, so x has to be greater than 1.\r<BR>\n" );
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document.write( "7 = 4x - 5 is your second equation.<BR>\n" );
document.write( "add 5 to both sides to get 12 = 4x<BR>\n" );
document.write( "divide both sides by 4 to get x = 3.<BR>\n" );
document.write( "when x = 3, 4x - 5 = 7<BR>\n" );
document.write( "x can't be equal to 3, because then f(x) would be equal to 7 and that's not in the range, so x has to be smaller than 1.\r<BR>\n" );
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document.write( "your domain is 1 < x < 3\r<BR>\n" );
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document.write( "this will lead to a range -1 < f(x) < 7\r<BR>\n" );
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document.write( "your graph will look something like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-5%2C5%2C-12%2C12%2C4x-5%2C-1%2C7%2C200%28x-1%29%2C200%28x-3%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-5%2C5%2C-12%2C12%2C4x-5%2C-1%2C7%2C200%28x-1%29%2C200%28x-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the vertical lines are at x = 1 and 3 to show where the value of x has to be  between, but not at.\r<BR>\n" );
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document.write( "the horizontal lines are at y = -1 and 7 to show where the value of y has to be between, but not at.\r<BR>\n" );
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document.write( "you can see from the intersection of the vertical and horizontal lines, that the line of the equation meets at those points.  <BR>\n" );
document.write( "this confirms that the limits of the domain create the limits of the range.\r<BR>\n" );
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