A sports trainer has monthly costs of \( \$ 67.67 \) for phone service and \( \$ 44.42 \) for a website and advertising. In addition, a \( \$ 15 \) fee is paid to the gym for each session in which the trainer works with a client. Part: \( \mathbf{0} / 4 \) Part 1 of 4 (a) Write a cost function to represent the cost \( C(x) \) for \( x \) training sessions. \[ C(x)= \]

To find the cost function \( C(x) \) for the sports trainer, we first combine the fixed monthly costs with the variable costs incurred for each training session. The fixed costs include the phone service and the website and advertising: \[ 67.67 + 44.42 = 112.09 \] The variable cost is \( 15 \) dollars for each training session \( x \). Thus, the cost function can be expressed as: \[ C(x) = 112.09 + 15x \] This function represents the total cost \( C(x) \) as a combination of both fixed and variable costs depending on the number of sessions \( x \). For anyone who loves sports or business, understanding cost functions is vital! They help trainers and fitness professionals budget their finances while setting prices that cover their costs and support their growth. So, the next time you think about training, remember the numbers behind the scenes! To optimize profits, it's essential to track fixed and variable costs closely! Common mistakes include neglecting to factor in all expenses or miscalculating variable costs. A tip? Always revisit your cost function regularly and update it as your costs change, ensuring you never underestimate those training session fees!