myfunctionx

myfunctionx is a generic mathematical function commonly used in tutorials and software libraries to illustrate polynomial evaluation. In its typical implementation, myfunctionx computes a quadratic polynomial of the form f(x) = a*x^2 + b*x + c, where a, b, and c are optional parameters. The function is designed to accept scalar inputs as well as one-dimensional arrays or lists, returning a result of the same shape as the input.

Definition and signature: A representative signature is myfunctionx(x, a=1, b=0, c=0). If x is a scalar, the function returns a scalar; if x is a vector, the operation is applied element-wise, yielding a vector of the same length.

Behavior and properties: The function is deterministic; given the same inputs it always returns the same output. It is differentiable for all real x. The output can be real or complex depending on the input and parameter choices. Non-numeric inputs typically raise a type error or yield NaN, and non-finite values propagate according to the language’s rules. Implementations may optimize with vectorized operations to achieve linear time in the number of elements, O(n).

Examples: Myfunctionx(2) with default parameters yields 4. Myfunctionx([1, 2, 3], a=2, b=-1, c=0) yields [1, 6, 15], since f(1)=1, f(2)=6, f(3)=15.

Related topics: The function is a standard demonstration of polynomial evaluation and is often contrasted with functions that apply nonlinearity or piecewise behavior.