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Given two sets X and Y, a binary relation f between X and Y is a function (from X to Y) if for every element x in X there is exactly one y in Y such that f relates x to y. The sets X and Y are called the domain and codomain of f, respectively. The image of the function f is the subset of Y consisting of only those elements y of Y such that ...
In this case, the domain is represented on the x-axis of the graph, as the projection of the graph of the function onto the x-axis. For a function :, the set Y is called the codomain: the set to which all outputs must belong. The set of specific outputs the function assigns to elements of X is called its range or image. The image of f is a ...
In mathematics, a quadratic function of a single variable is a function of the form [1] = + +,,where is its variable, and , , and are coefficients.The expression + + , especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two.
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
The solutions of the quadratic equation ax 2 + bx + c = 0 correspond to the roots of the function f(x) = ax 2 + bx + c, since they are the values of x for which f(x) = 0. If a , b , and c are real numbers and the domain of f is the set of real numbers, then the roots of f are exactly the x - coordinates of the points where the graph touches the ...
A function :, with domain X and codomain Y, is bijective, if for every y in Y, there is one and only one element x in X such that y = f(x). In this case, the inverse function of f is the function f − 1 : Y → X {\displaystyle f^{-1}:Y\to X} that maps y ∈ Y {\displaystyle y\in Y} to the element x ∈ X {\displaystyle x\in X} such that y = f ...
Functions of the form = have at most one -intercept, but may contain multiple -intercepts. The x {\displaystyle x} -intercepts of functions, if any exist, are often more difficult to locate than the y {\displaystyle y} -intercept, as finding the y {\displaystyle y} -intercept involves simply evaluating the function at x = 0 {\displaystyle x=0} .
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation. Other ways of ...
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