# Function with point of resistance

• rhenretta
In summary, the conversation discusses the concept of a function, f(x), that wants to equalize at a value of 3,000,000. The function experiences exponential resistance when it goes above this value and exponential growth when it goes below. The speaker is struggling to understand how this function would look like and proposes using another function, g(x), to represent it. Two equations are provided to demonstrate the behavior of f(x) depending on the value of g(x).
rhenretta
My maths is failing me. Take f(x), where f(x) wants to equalize at a value of 3,000,000. If it goes above, there is exponential resistance bringing it down, and as it goes below there is exponential growth driving it up. What would f(x) look like?

This is driving me nuts!

How you state this problem it doesn't make much sense. From what I understand you want to have a function that will change over x but you also want it to have an tendency towards 3,000,000 over some other variable like time?

If you let g(x) be your function:

if g(x) <= 3,000,000 then f(t,x) = g(x) + t/(t+1)|3,000,000 – g(x)|
if g(x) > 3,000,000 then f(t,x) = g(x) - t/(t+1)|3,000,000 – g(x)|

Last edited:

## 1. What is a function with point of resistance?

A function with point of resistance is a mathematical concept that represents the relationship between two variables, where one variable increases or decreases in response to changes in the other variable. The point of resistance is the point at which the two variables intersect, and the function changes direction. This point is also known as the critical point or the equilibrium point.

## 2. How do you graph a function with point of resistance?

To graph a function with point of resistance, you first need to identify the equation of the function and the point of resistance. Then, plot the points on a coordinate plane and connect them with a smooth line. The point of resistance will be the point at which the line changes direction, either from increasing to decreasing or from decreasing to increasing.

## 3. What is the significance of the point of resistance in a function?

The point of resistance in a function is significant because it represents the balance or equilibrium between the two variables. It is the point at which the function changes direction, and it can indicate the maximum or minimum value of the function. The point of resistance is also useful in analyzing the behavior of the function and understanding the relationship between the variables.

## 4. How do you find the point of resistance in a function?

To find the point of resistance in a function, you can use various methods such as graphing, algebraic manipulation, or calculus. For simple functions, you can graph the function and identify the point of intersection. For more complex functions, you may need to use algebraic techniques such as solving systems of equations or finding the derivative to determine the critical point.

## 5. What are some real-world applications of functions with point of resistance?

Functions with point of resistance have many real-world applications, including in economics, physics, and biology. In economics, functions with point of resistance are used to model supply and demand, where the point of resistance represents the equilibrium price and quantity. In physics, functions with point of resistance can represent the motion of objects under the influence of forces. In biology, functions with point of resistance are used to model population growth and predator-prey relationships.

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