# Response Curve

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## Concept

A Response Curve is a mathematical formula that converts an input value into an output value.

## Components

The Response Curve is comprised of a curve type and 4 variables. By changing these values, we change the "shape" of the curve and, therefore, how it converts the raw number into a meaningful value for our utility.

### Curve Types

The curve types are:

- Linear
- Polynomial
- Logistic
- Logit
- Normal (for a normal distribution)
- Sine

### Variables

The 4 variables are, m, k, b, and c change their meanings slightly depending on the curve type.

For Linear and Polynomial types, they represent what we are used to seeing in the *y = mx + b* formula:

- m = slope (positive numbers for up, negative for down)
- k = exponent (1 = linear)
- b = y-intercept
- c = x-intercept

For Logistic curves, they are:

- m = slope of line in middle
- k = Vertical size and direction of curve (positive numbers for up, negative for down)
- b = moves line vertically from its starting point
- c = moves line horizontally from its starting point

For Normal curves, they are:

- m = width of the "bump" of the curve. Roughly equivalent to changing the standard deviation.
- k = height of the "bump"
- b = moves line vertically from its starting point
- c = moves line horizontally from its starting point

## Code

The data is held in the very simple ResponseCurve class but the calculations are performed in the Consideration class in **Consideration::GetConsiderationValue**.