SOLUTION: Please may you help me immediately to solve this problem: a.suppose the international airmail on articles/packets to countries in zone 1 are given below. Weight (w) cost in kina

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Question 1085943: Please may you help me immediately to solve this problem: a.suppose the international airmail on articles/packets to countries in zone 1 are given below.
Weight (w) cost in kina
Up to 50 55
Up to 150 110
Up to 250 180
Up to 1kg 290
Up to 2kg 450
i.write the cost function,in function notation for the above.
ii.Draw the graph of this function
iii.state the domain and range of this function
iv.does the graph really represent a function? Justify you answer.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Part i)

The cost function is the piecewise function given below

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

The piecwise function basically says

c(w) = 55 if
OR
c(w) = 110 if
OR
c(w) = 180 if
OR
c(w) = 290 if
OR
c(w) = 450 if

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 here. 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 step function

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Part iii)

Domain: set of real numbers w such that

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

-------

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 vertical line test.

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