document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196402>Question 1196402</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the domain and range of function f(x)=3x-2 and sketch a graph for this<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 #829234 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=829234\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Domain = All real numbers<BR>\n" );
document.write( "Range = All real numbers\r<BR>\n" );
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document.write( "As an inequality we can say<BR>\n" );
document.write( "Domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity+%3C+x+%3C+infinity ALIGN=MIDDLE  ALT=\"-infinity+%3C+x+%3C+infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Range is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity+%3C+y+%3C+infinity ALIGN=MIDDLE  ALT=\"-infinity+%3C+y+%3C+infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The interval notation for each is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (-\infty, \infty)\"> to represent going from negative infinity to positive infinity. Use curved parenthesis for both types of infinity. This is because we cannot reach these endpoints. \r<BR>\n" );
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document.write( "The domain represents the set of possible inputs.<BR>\n" );
document.write( "The range represents the set of possible outputs.\r<BR>\n" );
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document.write( "To graph this, we need two points to draw a straight line\r<BR>\n" );
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document.write( "Compare the equation y = 3x-2 to the form y = mx+b<BR>\n" );
document.write( "m = 3 = 3/1 = slope<BR>\n" );
document.write( "b = -2 = y intercept\r<BR>\n" );
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document.write( "The y intercept b = -2 tells us that (0,-2) is one point on the line<BR>\n" );
document.write( "Then move up 3 and to the right 1 (based on what the slope says) to arrive at the point (1,1)<BR>\n" );
document.write( "Therefore, you can draw a straight line through (0,-2) and (1,1) to graph out y = 3x-2<BR>\n" );
document.write( "You don't have to start at the anchor point of (0,-2) as you can start anywhere you like. But you have to be on the line. \r<BR>\n" );
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document.write( "Another way to graph:<BR>\n" );
document.write( "Plug in x = 0 to find that...<BR>\n" );
document.write( "y = 3x-2<BR>\n" );
document.write( "y = 3(0)-2<BR>\n" );
document.write( "y = 0-2<BR>\n" );
document.write( "y = -2<BR>\n" );
document.write( "Therefore, the ordered pair (x,y) = (0,-2) is on the line\r<BR>\n" );
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document.write( "Repeat for x = 1<BR>\n" );
document.write( "y = 3x-2<BR>\n" );
document.write( "y = 3(1)-2<BR>\n" );
document.write( "y = 3-2<BR>\n" );
document.write( "y = 1<BR>\n" );
document.write( "So (x,y) = (1,1) is another ordered pair point.<BR>\n" );
document.write( "We get (0,-2) and (1,1) like we found earlier.  \r<BR>\n" );
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document.write( "There's nothing particularly special about x = 0 and x = 1. You can pick any two x values you want. After all the domain is the set of all real numbers.<BR>\n" );
document.write( "I went with those values because they're small and easy to work with. Also, most standard xy grids are centered around the origin. <BR>\n" );
document.write( "Feel free to choose your favorite two numbers to use for x.\r<BR>\n" );
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document.write( "You can use graphing software to verify your work. I recommend it to check your work rather than do it entirely for you. <BR>\n" );
document.write( "Desmos and GeoGebra are two free options, among many others. <BR>\n" );
document.write( "Here's the link to the Desmos graph so you can interact with it.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.desmos.com/calculator/bawhrkdr7a\">https://www.desmos.com/calculator/bawhrkdr7a</a>\r<BR>\n" );
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document.write( "Take note how the graph stretches forever left and right. This visually confirms why the domain is the set of all real numbers. <BR>\n" );
document.write( "Any number can replace x. Hence we have infinitely many (x,y) points to work with. <BR>\n" );
document.write( "All points on this line are of the form (x, 3x-2) meaning that the y coordinate depends on what you picked for x.\r<BR>\n" );
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document.write( "Similarly, the graph stretches up and down forever. This means any output (y) is possible and it visually confirms why the range is the set of all real numbers. \r<BR>\n" );
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document.write( "The domain and range being \"all real numbers\" applies to any diagonal linear equation (i.e. when the slope is nonzero, and is defined).<BR>\n" );
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