Definition, Order, and Degree Definition: - Definition: The definition of a function is a mathematical relationship that expresses one variable (...
Definition:
Definition: The definition of a function is a mathematical relationship that expresses one variable (dependent variable) in terms of another variable (independent variable).
Examples:
f(x) = x^2 + 1
g(t) = sin(t)
Order:
Order: The order of a function tells us the highest power of each variable in the expression.
Examples:
f(x) = 2x^3 - 4x + 1 has order 3.
g(t) = t^2 + 3t - 1 has order 2.
Degree:
Degree: The degree of a function tells us the highest power of the independent variable in the expression.
Examples:
f(x) = 3x^2 - 2x + 1 has degree 2.
g(t) = t^4 + 2t^2 - 1 has degree 4.
Additional Notes:
The degree of a function is always less than or equal to the order of the function.
A function can be of order n and still have a lower degree than n.
The degree of a function can be used to determine the type of root it has