Question

Select the correct answer.
Charlotte has been working for her company for x years. The number of years Travis has been working for the same company, y years, is exactly 3 years longer than Charlotte.

What is the range of the relationship between x and y?

A.
y ≥ 0
B.
y ≥ 3
C.
y ≤ 3
D.
0 ≤ y ≤ 3

Answer 1

The relationship described indicates that Travis's years of service (y) is 3 years longer than Charlotte's years of service (x). This can be expressed with the equation:

\[ y = x + 3 \]

From this relationship:

1. Since "years worked" cannot be negative, Charlotte's years (x) must be greater than or equal to 0, which implies:
- \( x \geq 0 \)

2. If we substitute \( x = 0 \) into the equation, we get:
- \( y = 0 + 3 = 3 \)

3. As x increases, y will also increase. Therefore, the minimum value for y is 3, and it can continue to grow indefinitely as x increases.

Thus, the correct range for y based on the relationship with x is:

- The minimum value of y is 3 (when x is 0).
- There is no maximum limit for y since there is no upper constraint on x.

The only relevant constraint given is \( y \geq 3 \).

Based on this analysis, the correct answer is:

**B. y ≥ 3**