Question 73·Easy·Linear Functions
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?
For linear function questions where you’re given a formula and a specific input, immediately identify the input value (here, the number of miles) and substitute it into the function. Then, follow the order of operations: perform the multiplication (rate times input) first, then add or subtract any constant term. Watch for common traps like forgetting fixed fees or misreading the rate, and keep your arithmetic neat to avoid simple multiplication errors.
Hints
Identify what represents
In the function , think about what value should be for a 12-mile ride.
Substitute into the function
Once you know , replace in with that number and write out the new expression.
Do the arithmetic carefully
Evaluate the expression in two steps: first multiply by the number of miles, then add the fixed $3 fee.
Desmos Guide
Evaluate the expression in Desmos
In the Desmos calculator, type 2.5*12+3 and press Enter. The displayed value is the total cost of the 12-mile ride according to the function.
Step-by-step Explanation
Understand the function
The function gives the total cost in dollars of a taxi ride after traveling miles.
- The number is the cost per mile.
- The number 3 is the fixed starting fee (the pickup charge of $3).
Substitute the given number of miles
The question asks for the total cost of a 12-mile ride. That means .
Substitute into the function:
Calculate step by step
First, multiply by :
Now add the pickup fee of $3:
So, the total cost for a 12-mile ride is $33, which corresponds to answer choice C) $33.