To determine the correct answer, let's carefully analyze the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] given in the problem.
Charlotte has been working for her company for [tex]\( x \)[/tex] years. The number of years Travis has been working for the company, denoted as [tex]\( y \)[/tex], is exactly 3 years longer than Charlotte. Mathematically, this relationship can be written as:
[tex]\[ y = x + 3 \][/tex]
Our goal is to determine the range of values for [tex]\( y \)[/tex], given that [tex]\( x \)[/tex] can be any non-negative number (since the number of years someone has worked cannot be negative).
### Step-by-Step Analysis
1. Express the relationship: From the statement, [tex]\( y = x + 3 \)[/tex].
2. Determine the minimum value of [tex]\( x \)[/tex]: The smallest non-negative value [tex]\( x \)[/tex] can take is 0 (since [tex]\( x \geq 0 \)[/tex]).
3. Find the corresponding value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 0 + 3 \][/tex]
[tex]\[ y = 3 \][/tex]
Thus, the minimum value [tex]\( y \)[/tex] can take is 3.
4. Determine the range for [tex]\( y \)[/tex]: Since [tex]\( y \)[/tex] is always 3 years more than [tex]\( x \)[/tex] and [tex]\( x \)[/tex] starts from 0 and increases indefinitely, [tex]\( y \)[/tex] will start from 3 and increase indefinitely as well.
Therefore, the range of [tex]\( y \)[/tex] is:
[tex]\[ y \geq 3 \][/tex]
After examining the provided options:
A. [tex]\( y \geq 0 \)[/tex]
B. [tex]\( y \geq 3 \)[/tex]
C. [tex]\( y \leq 3 \)[/tex]
D. [tex]\( 0 \leq y \leq 3 \)[/tex]
The correct answer is:
B. [tex]\( y \geq 3 \)[/tex]
