webmaster makes \( \$ 24 \) an hour for the first 38 hours she works during a veek and \( \$ 31 \) an hour for each hour worked over 38 hours. Which piecewise equation models her total weekly pay \( y \) in dollars as it relates to the number f hours \( x \) that she has worked during the week?

To model the total weekly pay \( y \) in dollars as it relates to the number of hours \( x \) worked during the week, we can use a piecewise function. 1. For the first 38 hours, the pay is \( \$24 \) per hour. 2. For any hours worked over 38, the pay is \( \$31 \) per hour. The piecewise function can be defined as follows: \[ y(x) = \begin{cases} 24x & \text{if } 0 \leq x \leq 38 \\ 24 \cdot 38 + 31(x - 38) & \text{if } x > 38 \end{cases} \] ### Explanation: - For \( 0 \leq x \leq 38 \): The total pay is simply \( 24 \) times the number of hours worked, which is \( 24x \). - For \( x > 38 \): The total pay consists of the pay for the first 38 hours plus the pay for the additional hours worked. The pay for the first 38 hours is \( 24 \cdot 38 \), and for each hour beyond 38, the pay is \( 31 \) per hour, which is represented as \( 31(x - 38) \). This piecewise function accurately models the total weekly pay based on the number of hours worked.