Question 169171
"Marlena is making her own bracelets.  Each bracelet will have 10 beads. Write a function rule to describe the number of beads she will use.  Find a reasonable domain and range for the fuction if Marlena makes up to 7 bracelets."


We'll have "x" be the number of bracelets and "y" be the number of beads.


"Marlena makes up to 7 bracelets": because of this statement, we know that x, the number of bracelets, may not go over 7.


{{{x<=7}}}


Logically, Marlena cannot make a negative number of bracelets, so we also know that x has to be more than (or equal to) 0.


{{{x>=0}}}


So our logical domain would be:
{{{0<=x<=7}}}
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We know that each bracelet has ten beads, so the amount of beads used would be ten times the amount of bracelets, or {{{y=10x}}}---in f(x) form, this is the function----> {{{f(x)=10x}}}.


To get the logical range, all we have to do is use the logical domain, which we already have, and use the same inequality signs.


Plug in 7 and 0, our logical domain, for x to get the logical range, y.


{{{y<=10(7)}}}
{{{y<=70}}}


{{{y>=10(0)}}}
{{{y>=0}}}


So the logical range would be 
{{{0<=y<=70}}}
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Domain: {{{0<=x<=7}}}
Range: {{{0<=y<=70}}}