Question

Consider the first five terms of the following sequence.

2, 6, 18, 54, 162, ...
If the sequence defines a function, what is a reasonable domain and range of the function?
O A. Domain: all real numbers; Range: all real numbers
B. Domain: {1, 2, 3, 4, 5, ...}; Range: {2, 6, 18, 54, 162, ...}
C. Domain: {1, 2, 3, 4, 5, ...}; Range: all real numbers
O D. Domain: all real numbers; Range: {2, 6, 18, 54, 162, ...}

Answer 1

B. Domain: {1, 2, 3, 4, 5, ...}; Range: {2, 6, 18, 54, 162, ...}

Explanation:

2, 6, 18, 54, 162

This is a geometric sequence because it is increasing by multiplication. The common ration of the sequence is *3.

Our sequence values will serve as the y-values, or the range, and our x-values will be the term number.

Domain, or x-values: {1, 2, 3, 4, 5, ...}

Range, or y-values: {2, 6, 18, 54, 162, ...}

It is not A or D because we can't have negative term values. "All real numbers" implies all positive and negative integers.

The range also cannot be all real numbers for the same reason.