The problem states that the cable TV company charges $23 for the basic service plus $5 for each movie channel. We are asked to express the total cost $C(x)$ in terms of the number of movie channels $x$.

• The base fee is $23 (which is constant).
• For each movie channel, the company charges an additional $5.

So, the cost function is given by the sum of the fixed base fee and the variable cost per movie channel, which is:

$C(x) = 5x + 23$

Where:

• $x$ is the number of movie channels,
• $5x$ represents the cost of the movie channels, and
• 23 is the base fee.

Therefore, the correct answer is:

A. C(x) = 5x + 23

Would you like more details on how to derive such cost functions? Here are some related questions:

1. How would the cost function change if the base service fee was $30 instead of $23?
2. What if the company introduced a discount for multiple movie channels? How would that affect the cost function?
3. How can we interpret the slope of the cost function in real-life terms?
4. How would you calculate the total cost if someone subscribes to 3 movie channels?
5. Can the relationship between cost and the number of channels be modeled by a non-linear function?

Tip: Always check the structure of a cost function. A linear relationship means the cost increases or decreases at a constant rate.