At a local grocery store, the deli counter has bologna on sale for \( \$ 4.66 \) per pound with a limit of 1.82 pounds per customer. If \( y \) represents the total cost for buying \( x \) pounds of bologna, then which set of compound inequalities below represents the domain and range of this situation? \[ 0 \leq x \leq 8.48 \text { and } 0 \leq y \leq 1.82 \] \( 0 \leq x \leq 1.8 \) and \( 0 \leq y \leq 4.66 \) \( 0 \leq x \leq 4.66 \) and \( 0 \leq y \leq 1.82 \) \( 0 \leq x \leq 1.82 \) and \( 0 \leq y \leq 8.48 \)

The situation describes a limit on the pounds of bologna a customer can buy, which is 1.82 pounds. If we denote the total cost \( y \) based on the weight \( x \) in pounds, then the total cost can be calculated as \( y = 4.66x \). Thus, for \( x \) in the range of \( 0 \) to \( 1.82 \), the corresponding values of \( y \) will be \( 0 \leq y \leq 4.66 \), since buying the maximum allowed will yield that maximum cost! So, the correct set of compound inequalities representing the domain and range here would be \( 0 \leq x \leq 1.82 \) and \( 0 \leq y \leq 4.66 \). If you're still grappling with inequalities, think of them like a playground with fences! The fences ensure that the children (representing our variables) can only roam within certain boundaries. For bologna, our kids can't go over 1.82 pounds at the deli counter, and the total cost can’t jump over $4.66 either. Staying within these bounds is key to enjoying the bologna without overspending!