document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=361916>Question 361916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can you please explain the steps \r<BR>\n" );
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document.write( "state the domain of f(x)=9-18x\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257989 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=257989\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is f(x) = 9 - 18*x\r<BR>\n" );
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document.write( "your range is the set of values that f(x) can take\r<BR>\n" );
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document.write( "your domain is the set of values that x can take.\r<BR>\n" );
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document.write( "in this equation, x can be anything, so the domain is the set of all real numbers.\r<BR>\n" );
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document.write( "the two main reasons the domain would be restricted are:\r<BR>\n" );
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document.write( "square root of a negative number.\r<BR>\n" );
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document.write( "division by 0.\r<BR>\n" );
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document.write( "neither one give you a real number as an answer so the values of x that result in an equation with a negative square root or with a division of 0 would be excluded from the domain.\r<BR>\n" );
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document.write( "in your equation, none of that is happening.\r<BR>\n" );
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document.write( "x can be negative.<BR>\n" );
document.write( "x can be positive.<BR>\n" );
document.write( "x can be 0.\r<BR>\n" );
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document.write( "the domain is all real number of x.\r<BR>\n" );
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document.write( "an example of an equation where the domain cannot be the set of all real numbers would be:\r<BR>\n" );
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document.write( "f(x) = 1/x\r<BR>\n" );
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document.write( "the domain is all real number except x = 0 since when x is equal to 0, the result is undefined because division by 0 is infinity and infinity is not a real number.\r<BR>\n" );
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document.write( "another example:\r<BR>\n" );
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document.write( "f(x) = square root of x.\r<BR>\n" );
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document.write( "x cannot be negative so the domain is all real numbers that are not negative.\r<BR>\n" );
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document.write( "the graph of your equation of f(x) = 9 - 18*x is shown below:\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-10%2C10%2C-100%2C100%2C9-18%2Ax%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-100%2C100%2C9-18%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "it's a straight line where y gets more positive as x gets more negative, and y gets more negative as x gets more positive.\r<BR>\n" );
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document.write( "there is no discontinuity where the value of y can't be plotted.\r<BR>\n" );
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document.write( "the graph of the equation of y = 1/x is shown below:\r<BR>\n" );
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document.write( "you can see the discontinuity around x = 0.\r<BR>\n" );
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document.write( "as x approaches 0 from the negative side, the value of y tends towards infinity in a negative direction.\r<BR>\n" );
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document.write( "as x approaches 0 from the positive side, the value of y tends towards infinity in a positive direction.\r<BR>\n" );
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document.write( "the graph of y = square root of x is shown below:\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-50%2C50%2C-10%2C10%2Csqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-50%2C50%2C-10%2C10%2Csqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can see that the value of x are positive or 0 only.\r<BR>\n" );
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document.write( "once again, the domain is the set of values that x can take and the range is the set of values that f(x) can take.\r<BR>\n" );
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document.write( "the range is dependent on the equation that ties the value of f(x) to x.\r<BR>\n" );
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document.write( "in the first graph, the range is the set of all real numbers.\r<BR>\n" );
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document.write( "in the second graph, the range is the set of all real numbers except 0.\r<BR>\n" );
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document.write( "f(x) cannot be 0 because 1 / x will never be 0 no matter how large x gets.\r<BR>\n" );
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document.write( "it will be very small but never 0.\r<BR>\n" );
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document.write( "in the third graph, the range is the set of all real numbers greater than or equal to 0.\r<BR>\n" );
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document.write( "there's a wrinkle here that you probably need to be aware of.\r<BR>\n" );
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document.write( "if i give you an equation that says that y = square root of x, then you would take the positive square root of x only.\r<BR>\n" );
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document.write( "if i give you an equation that says that y^2 = x, and you are solving for y, then your answer would be +/- square root of x.\r<BR>\n" );
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document.write( "the difference is in what you are given.\r<BR>\n" );
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document.write( "the first equations states that you are to take only the positive square root of x.\r<BR>\n" );
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document.write( "the second equation states that you are to solve for y.  the solution is both positive square root of x and negative square root of x.\r<BR>\n" );
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document.write( "an example:\r<BR>\n" );
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document.write( "y^ = 25\r<BR>\n" );
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document.write( "y = +/- 5 because 5^2 = 25, and (-5)^2 = 25.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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