Question 1085943
<font color="black" face="times" size="3">Part i)


The cost function is the piecewise function given below


<img src = "https://i.imgur.com/QJcS5VQ.png">


where w is the weight in grams, and c(w) is the cost


The piecwise function basically says


c(w) = 55 if {{{0 <= w <= 50}}}
OR
c(w) = 110 if {{{50 < w <= 150}}}
OR
c(w) = 180 if {{{150 < w <= 250}}}
OR
c(w) = 290 if {{{250 < w <= 1000}}}
OR
c(w) = 450 if {{{1000 < w <= 2000}}}


so we have 5 separate functions depending on what w is. The notation given previously (with the big single curly brace) is a more compact way to write the piecewise function.


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Part ii)


The graph is shown <a href="https://i.imgur.com/kf35urK.png">here</a>. The graph was created with GeoGebra (free graphing software).


Note how points {C, E, G, I} are open circles to indicate we do NOT include them as part of the function


The graph represents a <a href="http://www.mathwords.com/s/step_function.htm">step function</a>


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Part iii)


Domain: set of real numbers w such that {{{0 <= w <= 2000}}}


basically saying that the weights can be as small as 0 grams or as large as 2000 grams (2 kg).


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Range: c(w) can be only values drawn from this set: {55, 110, 180, 290, 450} 


Those values are the given costs for each piece of the piecewise function (see part i)


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Part iv)


Yes it's a function because it passes the <a href="http://www.mathwords.com/v/vertical_line_test.htm">vertical line test</a>. 


For any given input, there is EXACTLY ONE output. This adds further confirmation that we have a function here.</font>