Question

amanda is a software saleswoman. let p be amanda’s total pay (in dollars). let n be the number of copies of english is fun she has sold. amanda has 120 copies available to sell. suppose that p = 40n + 3600 gives p as a function of n for these available copies. identify the correct description of the values in both the domain and range of the function. then, for each, choose the most appropriate set of values. | description of values | set of values | |---|---| | domain | ☐ number of copies amanda has sold | select | | ☐ amanda’s total pay (in dollars) | | | range | ☐ number of copies amanda has sold | select | | ☐ amanda’s total pay (in dollars) | |

Explanation:

Step1: Understand Domain and Range

The domain of a function is the set of input values (independent variable), and the range is the set of output values (dependent variable). Here, \( N \) (number of copies sold) is the input, \( P \) (total pay) is the output.

Step2: Domain Description

Domain values are the input, so "number of copies Amanda has sold" (since \( N \) is the input). The number of copies sold \( N \) can be from 0 to 120 (inclusive, as she has 120 copies available). So domain set: \( \{0, 1, 2, \dots, 120\} \) (non - negative integers from 0 to 120).

Step3: Range Description

Range values are the output, so "Amanda's total pay (in dollars)". The function is \( P = 40N+3500 \). When \( N = 0 \), \( P=3500 \); when \( N = 120 \), \( P = 40\times120 + 3500=4800 + 3500 = 8300 \). So the range is all values \( P=40N + 3500 \) where \( N\in\{0,1,\dots,120\} \), which are \( 3500,3540,3580,\dots,8300 \) (each time \( N \) increases by 1, \( P \) increases by 40).

Answer:

• Domain:
• Description: number of copies Amanda has sold
• Set of Values: \( \{0, 1, 2, \dots, 120\} \) (or non - negative integers from 0 to 120)
• Range:
• Description: Amanda's total pay (in dollars)
• Set of Values: \( \{3500, 3540, 3580, \dots, 8300\} \) (values of \( 40N + 3500 \) for \( N = 0,1,\dots,120 \))