document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084189>Question 1084189</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Give the domain and range for the general functions. Assume A>0.\r<BR>\n" );
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document.write( "h(x)=A tan (nx-b)  </SPAN>\n" );
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document.write( "Domain: <BR>\n" );
document.write( "The domain is the set of allowed inputs of this function. It is the set of allowed x values we can plug in.<BR>\n" );
document.write( "It turns out that tangent is undefined whenever the input is equal 90 degrees, 270 degrees, etc\r<BR>\n" );
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document.write( "In general, if the argument is equal to 180k+90, for any integer k, then the result will be undefined.\r<BR>\n" );
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document.write( "Set the argument equal to 180k+90 solve for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Ax+-+b+=+180k%2B90 ALIGN=MIDDLE  ALT=\"n%2Ax+-+b+=+180k%2B90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Ax+=+180k%2B90%2Bb ALIGN=MIDDLE  ALT=\"n%2Ax+=+180k%2B90%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28180k%2B90%2Bb%29%2Fn ALIGN=MIDDLE  ALT=\"x+=+%28180k%2B90%2Bb%29%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So if x is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28180k%2B90%2Bb%29%2Fn ALIGN=MIDDLE  ALT=\"%28180k%2B90%2Bb%29%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then n*x-b is equal to 180k+90.\r<BR>\n" );
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document.write( "Therefore, the domain is the set of x values such that x is a real number but x cannot equal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28180k%2B90%2Bb%29%2Fn ALIGN=MIDDLE  ALT=\"%28180k%2B90%2Bb%29%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using set builder notation, we'd write that as <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \mathbb{D}=\left\{x|x\in\mathbb{R} \ , \ x \neq \frac{180k+90+b}{n}\right\}\"><BR>\n" );
document.write( "where k is any integer.\r<BR>\n" );
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document.write( "Range: <BR>\n" );
document.write( "The range is the set of all real numbers. Notice how the graph of any tangent function has the graph stretch vertically on forever in both y directions.\r<BR>\n" );
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document.write( "Edit: I made the correction. Instead of 90k, it should be 180k+90 assuming you're working in degree mode. Other corrections are based on this. Apologies for any confusion. <BR>\n" );
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