Problem

Compare the domain and range of each function: \(C(n)=8n\) for integer \(0\le~n\le~10\) and \(C(x)=8x\) for real \(0\le~x\le~10\).

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For C(n)=8n, the domain is 0,1,2,3,4,5,6,7,8,9,10 and the range is 0,8,16,24,32,40,48,56,64,72,80 because n must be integers only; for C(x)=8x, the domain is [0,10] and the range is [0,80] because x can be any real number from 0 to 10.

For C(n)=8n, the domain is 0,8,16,24,32,40,48,56,64,72,80 and the range is 0,1,2,3,4,5,6,7,8,9,10 because multiplying by 8 switches the input and output values; for C(x)=8x, the domain is [0,80] and the range is [0,10].

Both functions have domain [0,10] and range [0,80] because they both use the rule 8 times the input and both start at 0 and end at 10.

For C(n)=8n, the domain is [0,10] and the range is 0,8,16,24,32,40,48,56,64,72,80 because the inputs go from 0 to 10 but the outputs only hit multiples of 8; for C(x)=8x, the domain is [0,10] and the range is [0,80].

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Compare the domain and range of each function: \(C(n)=8n\) for integer \(0\le~n\le~10\) and \(C(x)=8x\) for real \(0\le~x\le~10\).

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