document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253167>Question 253167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explanation of functions. I need to make a logo that I must create from functions I know. To get a good grade I must use functions that I haven't seen before. However, I am having a hard time understanding new functions over the internet. These are the functions that I know.<BR>\n" );
document.write( "-Linear (y=ax+b)<BR>\n" );
document.write( "-Quadratic (Parabole)<BR>\n" );
document.write( "-Absolute Value<BR>\n" );
document.write( "-Exponential<BR>\n" );
document.write( "-Square root<BR>\n" );
document.write( "-Rational (y=a/x-h +k)<BR>\n" );
document.write( "-... stairs one: y=a[b(x-h)]+k<BR>\n" );
document.write( "Sorry, I study in french and I hope this is clear enough. I need at least 2 new functions explained with detail please. I am allowed to use the circle. I think that will be a simple one. I must determine a Domain(?) and a Image(?) Hope I said it right. I need to be able to find the rule (?)for the function from the graphic and how I did it. If I don't get help before tuessday january 5th then I die :( Maybe you can just point me to a good simple site that explains functions well. I apreciate any help :) Dont consider my language as a problem I can learn the terms you use fast. 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 #185476 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=185476\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Joyeau anniversarie? my French is very bad . . \r<BR>\n" );
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document.write( "Let's give you a cubic function and a circle.<BR>\n" );
document.write( "First the cubic function can be expressed as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a%28x-h%29%5E3+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a%28x-h%29%5E3+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where h,k is a \"locator point\".<BR>\n" );
document.write( "The domain of this is all reals.<BR>\n" );
document.write( "The range of this is all reals.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "Second the circle function can be expressed as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-h%29%5E2%2Fa%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28x-h%29%5E2%2Fa%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-k%29%5E2%2Fb%5E2%29 ALIGN=MIDDLE  ALT=\"%28%28y-k%29%5E2%2Fb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where the center is h,k and a = b.<BR>\n" );
document.write( "The domain of a circle is from -h to +h and the range is from -k to +k.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "Back to your other functions:<BR>\n" );
document.write( "linear (Y = mX + b)<BR>\n" );
document.write( "domain: all reals, assuming it is not vertical.<BR>\n" );
document.write( "range: all reals<BR>\n" );
document.write( "--<BR>\n" );
document.write( "quadratic (y + aX^2 + bX + c)<BR>\n" );
document.write( "if opens up,<BR>\n" );
document.write( "domain: all reals<BR>\n" );
document.write( "range: y >= f(-b/2a)<BR>\n" );
document.write( "if opens down,<BR>\n" );
document.write( "domain : all reals<BR>\n" );
document.write( "range: y <= f(-b/2a)<BR>\n" );
document.write( "--<BR>\n" );
document.write( "absolute value (y = a/x-h/ + k)<BR>\n" );
document.write( "works the same as parabola.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "exponential (y = a*e^(x))<BR>\n" );
document.write( "growth has locator point at (0,a)<BR>\n" );
document.write( "domain: all reals<BR>\n" );
document.write( "range: y > 0.<BR>\n" );
document.write( "horizontal asymptote at y = 0<BR>\n" );
document.write( "decay has locator point at (0,a)<BR>\n" );
document.write( "domain: all reals<BR>\n" );
document.write( "range: y > 0.<BR>\n" );
document.write( "horizontal asymptote at y = 0<BR>\n" );
document.write( "--<BR>\n" );
document.write( "square root Y = asqrt(x-h) + k<BR>\n" );
document.write( "locator point is at (h,k)<BR>\n" );
document.write( "domain: x >= h<BR>\n" );
document.write( "range: y >=0.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "rational functions y = p(x) / q(x)<BR>\n" );
document.write( "Domain is a bit tricky here.<BR>\n" );
document.write( "question #1 - is the variable in the denominator?<BR>\n" );
document.write( "If yes, the denominator not = 0 and solve for x.<BR>\n" );
document.write( "If no, then <BR>\n" );
document.write( "question #2 - is the variable in a square root?<BR>\n" );
document.write( "If yes, then square root information >= 0and solve for x.<BR>\n" );
document.write( "If no, then you have answered no two times and can say domain all reals.<BR>\n" );
document.write( "range: <BR>\n" );
document.write( "If the degree of the numerator is > degree of denominator, then range: all reals.<BR>\n" );
document.write( "If the degree of the numerator is = degree of denominator, then range: coefficient numbers.<BR>\n" );
document.write( "If the degree of the numerator is < degree of denominator, then range: can't equal 0.\r<BR>\n" );
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document.write( "I hope that helps.<BR>\n" );
document.write( " </SPAN>\n" );
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