document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891575>Question 891575</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tell whether the function is linear. Then evaluate the function for the given value of x. The function is f(x) = x + 5; f(-2) \r<BR>\n" );
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document.write( "My work: \r<BR>\n" );
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document.write( "-2x = x + 5<BR>\n" );
document.write( "-1x     -1x<BR>\n" );
document.write( "-3x  =   5<BR>\n" );
document.write( "-3x/-3   =   5/-3<BR>\n" );
document.write( "x   =   -5/3 \r<BR>\n" );
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document.write( "However, I'm not sure if I solved that correctly, and I don't know how to fid out if its a linear or not. Thanks for your help!!!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539842 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=539842\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given;<BR>\n" );
document.write( "(1)  f(x) = x + 5<BR>\n" );
document.write( "This is linear because the variable, x, occurs in the function (named f) to the first power. If you had x^2, it would not be linear. Another view of linear is that the function is a straight line. In this case the line has a slope of 1 and the intercept of 5. Think of letting y = f(x), then you have the familiar equation of a straight line in the slope/intercept form, or y = x + 5. In algebra, linear means a straight line.<BR>\n" );
document.write( "To evaluate a function at a particular value of the argument, x in this case, simply substitute that value for x where ever it appears in the definition of the function.<BR>\n" );
document.write( "In this case we want f(x) as given in (1), when x = -2, or<BR>\n" );
document.write( "(2) f(-2) = (-2) + 5 or<BR>\n" );
document.write( "(3) f(-2) = 3<BR>\n" );
document.write( "See where you went wrong?<BR>\n" );
document.write( "If you wanted f(17), you have<BR>\n" );
document.write( "(4) f(17) = 17 + 5 or<BR>\n" );
document.write( "(5) f(17) = 22<BR>\n" );
document.write( "Get it?<BR>\n" );
document.write( "PS A function does not have to be linear to get its value at a certain argument. By the way, the argument is anything within the parentheses of the function's name. For example we could for the function in (1) get<BR>\n" );
document.write( "(6) f(c-3) = (c-3) + 5 or<BR>\n" );
document.write( "(7) f(c-3) = c +2<BR>\n" );
document.write( "If we had the (non-linear) function<BR>\n" );
document.write( "(8) g(x) = (x^3 - 2x^2)/3<BR>\n" );
document.write( "We get<BR>\n" );
document.write( "(9) g(-1) = ((-1)^3 - 2(-1)^2)/7 or<BR>\n" );
document.write( "(10) g(-1) = (-1 - 2)/3 or<BR>\n" );
document.write( "(11) g(-1) = -1<BR>\n" );
document.write( "Hope this helps, you'll use functions a lot in your future.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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