document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250253>Question 250253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me help my daughter solve this homework problem.\r<BR>\n" );
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document.write( "For a car traveling at a constant rate of 60 mi/h, the distance traveled is a function of the time traveled.\r<BR>\n" );
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document.write( "a. Express this relation as a function<BR>\n" );
document.write( "b Find the range of the function when the domain is [1,5,10]<BR>\n" );
document.write( "c What do the domain and range represent?\r<BR>\n" );
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document.write( "I am thinking that the expressed function should be something like<BR>\n" );
document.write( "f(d) = (60m)h\r<BR>\n" );
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document.write( "We can solve b. once we can figure out how to express it as a function.\r<BR>\n" );
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document.write( "Thank you 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 #182180 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=182180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. The basic equation that relates distance, rate and time for travel at a constant (or average) speed is: d = rt. To write this as a function for travel at a speed of 60 we would write:<BR>\n" );
document.write( "f(t) = 60t<BR>\n" );
document.write( "or perhaps<BR>\n" );
document.write( "d(t) = 60t<br><BR>\n" );
document.write( "b. & c. Domain is the set of possible values for the independent variable of a function. In other words the domain is the set of possible inputs to a function. The range is the set of possible outputs from a function. Since the outputs of a function are determined by its inputs, one must know the domain of a function to be able to find its range.<br><BR>\n" );
document.write( "A domain of [1,5,10] makes no sense. I am going to assume that it is [1.5, 10]. This notation is called interval notation. Interval notation is a shorthand way to express a contiguous set of numbers. This particular notation says the domain is the set of all the numbers between 1.5 and 10, including 1.5 and 10. (A parenthesis on either end (or both ends) of the notation means the number at that end is <b>not</b> included in the set. So an interval of (4, 20] would indicate all the numbers between 4 and 20, including 20 but not including 4.)<br><BR>\n" );
document.write( "Now that we know the domain we can figure out the range. Since the function f(t) = 60t is a linear function (i.e its graph is a line), then we can find the range by finding the outputs for the endpoints of the domain:<BR>\n" );
document.write( "f(1.5) = 60(1.5) = 90<BR>\n" );
document.write( "f(10) = 50(10) = 500<BR>\n" );
document.write( "So, if the domain is [1.5, 10], the range is [90, 500] </SPAN>\n" );
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