Final answer:
To find a curve that passes through a given point and has an arc length, we need to consider the characteristics of different types of functions. The correct answer is a linear function.
Step-by-step explanation:
The question asks us to find a curve that passes through a given point and has an arc length. The options given are linear function, exponential function, trigonometric function, and polynomial function. To find the correct answer, we need to understand how each type of function affects the arc length.
A linear function will always have a constant rate of change, so the arc length will increase or decrease at a constant rate. An exponential function will have a rapid increase in arc length as the input value increases. A trigonometric function will oscillate and have a periodic pattern, which will affect the arc length. A polynomial function can have varying rates of change depending on the degree of the polynomial.
Based on these characteristics, the correct answer is A) Linear function.