Detecting Intersections of Functions: Is There a Foolproof Method?

In summary, the conversation discusses the possibility of detecting the intersection of two functions and determining if the total points of intersection are finite or infinite. It is suggested to use the difference of the functions and find its zeros through a numerical method, such as Newton-Raphson, although this may not work for all functions. There is no known general algorithm for this task. Additionally, the possibility of detecting intersections when rotating the plot around a third axis is brought up.
  • #1
Physt
49
1
Does anyone know of an algorithm to detect the intersection of any two functions - both for individual points within a fixed range of x values and determining whether or not total points of intersection are finite or infinite over an infinite range of x values? Also, is this possible to do this when you rotate the plot around a third axis (such as using a graph for each edge of a polygon).
 
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  • #2
Well, the simplest is probably to take the difference of the functions and find its zeros, by some numerical method such as Newton-Raphson. It works only for reasonably nice functions, though. There is certainly no general algorithm that always works.
 

1. What is the intersection of two functions?

The intersection of two functions is the point or points where the two functions intersect or cross each other on a graph. In other words, it is the solution to the system of equations formed by the two functions.

2. How do you find the intersection of two functions?

To find the intersection of two functions, you can set the two functions equal to each other and then solve for the variable. You can also graph the two functions and determine the intersection point visually.

3. Can two functions intersect more than once?

Yes, two functions can intersect more than once. In fact, there can be infinite points of intersection if the two functions are identical. However, if two different functions intersect more than once, those points of intersection are often referred to as "multiple intersections."

4. What does it mean if two functions do not intersect?

If two functions do not intersect, it means that there is no solution to the system of equations formed by the two functions. In other words, there is no value of the variable that satisfies both equations simultaneously.

5. Can two functions intersect at a point other than on the x or y axis?

Yes, two functions can intersect at a point other than on the x or y axis. In fact, two functions can intersect at any point on a graph as long as they both pass through that point. The x and y intercepts are just the most common points of intersection that are discussed.

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