Linear Function
f(x) = mx + bDomain: ]-∞; ∞[Range: ]-∞; ∞[
A linear function is a type of function, which is defined as a polynomial function of degree one, and represents a straight line on a coordinate plane. This means that the graph of a linear function is a straight line.
The general form of a linear function is f(x) = mx + b, where m is the slope of the line, and b is the y-intercept. The slope represents the rate of change of the function, or the steepness of the line, and can be calculated as the change in y divided by the change in x between any two points on the line. The y-intercept represents the value of the y-axis where the line intersects with it, when x = 0.
Linear functions are commonly used in algebra, geometry and calculus. They can be used to model and solve problems related to a wide range of real-life situations, such as linear regression analysis, cost analysis, and profit maximization. Linear functions can also be used to approximate more complex functions through linearization, allowing for easier analysis and approximation of more complex models.
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