document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187171>Question 1187171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the x-intercepts (horizontal intercepts) of the function:  <BR>\n" );
document.write( "f(x)=4|x−3|−1\r<BR>\n" );
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document.write( "The intercepts are at  x= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818099 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the x-intercept is the value of x when the value of y = 0.\r<BR>\n" );
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document.write( "the equation is f(x) = 4 * |x - 3| - 1.<BR>\n" );
document.write( "set y = f(x) and the equation becomes y = 4 * |x - 3| - 1.<BR>\n" );
document.write( "set y equal to 0 and the equation becomes 0 = 4 * |x - 3| - 1.<BR>\n" );
document.write( "this is the same as 4 * |x - 3| - 1 = 0.<BR>\n" );
document.write( "add 1 to both sides of the equation to get 4 * |x - 3| = 1.<BR>\n" );
document.write( "divide both sides of the equation by 4 to get |x - 3| = 1/4.<BR>\n" );
document.write( "when the expression within the absolute value sign is positive, the equation becomes x - 3 = 1/4.<BR>\n" );
document.write( "add 3 to both sides to get x = 3 + 1/4 = 13/4.<BR>\n" );
document.write( "when the expression within the absolute value sign is negative, the equation becomes -(x-3) = 1/4.<BR>\n" );
document.write( "simplify to get -x + 3 = 1/4<BR>\n" );
document.write( "subtract 3 from both sides to get -x = -3 + 1/4<BR>\n" );
document.write( "multiply both sides by -1 to get x = 3 - 1/4 = 2 + 3/4 = 11/4.\r<BR>\n" );
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document.write( "the x-intercept should be x = 11/4 or and x = 13/4.\r<BR>\n" );
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document.write( "when x = 11/4, the equation becomes f(x) = 4 * abs(11/4 - 3) - 1 which becomes f(x) = 4 * abs(11/4 - 12/4) - 1 which becomes f(x) = 4 * 1/4 - 1 which becomes f(x) = 0.<BR>\n" );
document.write( "when x = 13/4, the equation becomes f(x) = 4 * abs(13/4 - 3) - 1 which becomes f(x) = 4 * abs(13/4 - 12/4) - 1 which becomes f(x) = 4 * 1/4 - 1 which becomes f(x) = 0.\r<BR>\n" );
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document.write( "both values of x are confirmed to be good.\r<BR>\n" );
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document.write( "your solution is that the y-intercepts are at x = 11/4 and x = 13/4.\r<BR>\n" );
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document.write( "abs(x-3) means the same thing as |x-3|.\r<BR>\n" );
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document.write( "the equation was graphed and is shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/110302.jpg\" >\r<BR>\n" );
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document.write( "11/4 = 2.75 as shown on the graph.<BR>\n" );
document.write( "13/4 = 3.25 as shown on the graph.<BR>\n" );
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