document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126702>Question 126702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hey again..\r<BR>\n" );
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document.write( "I'm working on the section inverse relations and functions and have a question.  Heres the problem.\r<BR>\n" );
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document.write( "Find the inverse of the function y=4x-7.  Is the inverse a function? \r<BR>\n" );
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document.write( "I found the inverse... its y=x+7/4    I just dont know if its a function or not?  \r<BR>\n" );
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document.write( "Thank you for helping </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92840 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=92840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Check your answer again.<BR>\n" );
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document.write( "You are given the function:<BR>\n" );
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document.write( "y = 4x - 7<BR>\n" );
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document.write( "To find the inverse of this, replace y with x and x with y to get:<BR>\n" );
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document.write( "x = 4y - 7<BR>\n" );
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document.write( "Solve this for y. Begin by transposing the equation (just swapping sides to get the term<BR>\n" );
document.write( "containing y on the left side). After transposing, the equation is:<BR>\n" );
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document.write( "4y - 7 = x<BR>\n" );
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document.write( "Get rid of the -7 on the left side by adding 7 to both sides to get:<BR>\n" );
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document.write( "4y = x + 7<BR>\n" );
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document.write( "Then solve for y by dividing both sides of this equation by 4 to get:<BR>\n" );
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document.write( "y = (1/4)x + 7/4<BR>\n" );
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document.write( "This is the inverse of the function y = 4x - 7.<BR>\n" );
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document.write( "That may have been the answer you got. If so you should have written it as:<BR>\n" );
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document.write( "y = (x + 7)/4 <BR>\n" );
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document.write( "so that it was clear that both terms, the x and the 7, were to be divided by 4. According to<BR>\n" );
document.write( "the rules of algebra, the way you wrote the answer, only the 7 was divided by 4 and x was then <BR>\n" );
document.write( "added to the result of that division so that the answer was x + (7/4).<BR>\n" );
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document.write( "Now, how do you tell whether or not that the inverse is a function? Look at the answer:<BR>\n" );
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document.write( "y = (1/4)x + (7/4)<BR>\n" );
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document.write( "This is in the form of a slope intercept equation ... the slope is (1/4) and the y-intercept<BR>\n" );
document.write( "is at +7/4 on the y-axis. The graph is a straight line. ... And the graph looks like this:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-15%2C15%2C+-15%2C15%2C%281%2F4%29%2Ax+%2B+%287%2F4%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-15%2C15%2C+-15%2C15%2C%281%2F4%29%2Ax+%2B+%287%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "One way to tell if this is a function is if you can draw a vertical line anywhere on<BR>\n" );
document.write( "the graph and it only intersects the graphed line at a maximum of one point, the graphed line <BR>\n" );
document.write( "represents a function.  On the graph shown above, anywhere you draw a vertical line it will cross the <BR>\n" );
document.write( "graphed line only at one point, so you have a function. If somewhere on the graph a <BR>\n" );
document.write( "vertical line could cross the graphed line at more than one point, then the graph would<BR>\n" );
document.write( "not represent a function.<BR>\n" );
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document.write( "So the answer to your problem is yes ... the inverse is a function.<BR>\n" );
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document.write( "Hope this helps you to understand one way of determining whether an expression represents <BR>\n" );
document.write( "a function.<BR>\n" );
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