Mercy participates in a bowling league on a team with her friends The cost of ordering team shirts can be represented by f(x)=12.75x+3.50 where the total cost is a function of x, the number of shirts ordered.Mercy's team must have a minimum of 6 players and a maximum of 10 players. Which is a reasonable range for the situation? All real numbers 80leqslant xleqslant 131 80,92.75,105.5,118.25,131 ygt 80

## Step 1<br />The problem involves a linear function, which is a function of the form \(f(x) = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. In this case, the function is \(f(x) = 12.75x + 3.50\), where \(x\) represents the number of shirts ordered and \(f(x)\) represents the total cost.<br /><br />## Step 2<br />The problem also provides a range for \(x\), which is the number of shirts ordered. The team must order between 6 and 10 shirts, inclusive. This means that \(x\) is restricted to the interval [6, 10].<br /><br />## Step 3<br />To find the reasonable range for the situation, we need to substitute the values of \(x\) into the function and calculate the corresponding \(f(x)\) values.<br /><br />## Step 4<br />Substitute \(x = 6\) into the function:<br />### \(f(6) = 12.75*6 + 3.50 = 80\)<br /><br />## Step 5<br />Substitute \(x = 10\) into the function:<br />### \(f(10) = 12.75*10 + 3.50 = 131\)<br /><br />## Step 6<br />Therefore, the reasonable range for the situation is [80, 131], which corresponds to option B.