A taxi company charges $3 for the initial pickup plus $2.50 per mile traveled. The total cost, in dollars, for a ride after traveling miles can be represented by the function . What is the total cost for a 12-mile ride?
A function turns an input into an output; in a taxi-cost rule, miles are the input and dollars are the output. When the trip length is given, enter the rule in Desmos and evaluate it at that mileage. Multiply the per-mile charge by the miles, but add the pickup fee only once.
Hints
- Hint 1
A function’s input goes inside its parentheses. Here the input measures miles. For a 12-mile ride, what number belongs inside ?
- Hint 2
A fixed fee is paid once, regardless of distance. Multiply the per-mile charge by the miles traveled, then add the pickup fee. Which term in the rule is that fee?
Step-by-step
Evaluate the cost function
Step 1Identify the input
The input counts miles, so a 12-mile ride asks for . That function value is the cost in dollars.
- Step 2
Enter the cost rule
The $2.50 charge applies to each mile, while the $3 pickup fee is paid once. Multiply the per-mile charge by the mileage, then add the pickup fee. Type in Desmos, using for miles and for cost. This defines the rule for the next line.
- Step 3
Find the fare
Type on the next line to put 12 miles into the rule. Desmos shows , so the total cost of the ride is $33. Choice C.