Taxicab fees A taxicab ride costs $3.50 plus $2.50 per mile for the first 5 miles, with the rate dropping to $1.50 per mile after the fifth mile. Let m be the distance (in miles) from the airport to a hotel. Find and graph the piecewise linear function c(m) that represents the cost of taking a taxi from the airport to a hotel m miles away.

Verified step by step guidance

1. Step 1: Understand the problem by identifying the different cost components for the taxi ride. The initial cost is $3.50, and the cost per mile changes after 5 miles.
2. Step 2: Define the piecewise function c(m) for the cost. For the first 5 miles, the cost is $3.50 plus $2.50 per mile. For distances greater than 5 miles, the cost is $3.50 plus $2.50 per mile for the first 5 miles, and $1.50 per mile for any additional miles.
3. Step 3: Write the piecewise function c(m). For 0 <= m <= 5, c(m) = 3.50 + 2.50m. For m > 5, c(m) = 3.50 + 2.50*5 + 1.50*(m - 5).
4. Step 4: Simplify the expression for m > 5. Calculate the cost for the first 5 miles and then add the cost for the additional miles.
5. Step 5: Graph the piecewise function. Plot the linear segment for 0 <= m <= 5 and the linear segment for m > 5, ensuring continuity at m = 5.