The curve of mathematical function has many meanings. In mathematics, a function is a relationship that maps each element in one set to each element in another set. Therefore, the image of the function is the mapping relationship between these elements. For example, the image of sine function is a continuous curve with a period of 2π, which represents the ordinate values corresponding to all angle values on the unit circle. Similarly, the image of exponential function is also a continuous curve with a period of 1, which represents the y values corresponding to all real numbers x in rectangular coordinate system.

In addition, functions can also be used to describe physical phenomena and economic phenomena. For example, in physics, Newton's second law can be written as f=ma, where f represents the resultant force acting on an object, m represents the mass of the object, and a represents the acceleration of the object. This formula describes the relationship between the force acting on an object when it is moving and its mass and acceleration. Therefore, we can rewrite this formula into a set of equations about the relationship between time t and position x, y and z:

$$begin{cases}

x=v_0t+frac{ 1}{2}at^2

y=v_0t+frac{ 1}{2}at^2

z=v_0t+frac{ 1}{2}at^2

End {cases}$$

Where v0 stands for initial velocity and a stands for acceleration. This set of equations describes the path taken by an object when it moves in a straight line under the constant external force.