What is f(x)?

f(x) notation represents a function.

• Definition: In mathematics, a Function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

• Input/Argument (x): The x inside the parentheses is the input or argument of the function. It represents the value you're feeding into the function.

• Output/Value (f(x)): f(x) represents the output or value of the function when the input is x. It is the result of applying the function's rule to the input x.

• Function Rule: The f part of f(x) represents the name of the function. The function itself has a rule or formula that tells you how to take the input x and produce the output f(x). For example, if f(x) = x^2 + 3, the function's rule is to square the input and add 3.

• Domain and Range: A Function has a domain, which is the set of all possible input values (x) for which the function is defined. It also has a range, which is the set of all possible output values (f(x)) that the function can produce.

• Graphing: Functions can be visually represented by Graph on a coordinate plane. The input x is usually plotted on the horizontal axis (x-axis), and the output f(x) is plotted on the vertical axis (y-axis). This creates a set of ordered pairs (x, f(x)) that form the graph of the function.

• Examples:

  • f(x) = 2x + 1 (Linear function)
  • g(x) = x^2 (Quadratic function)
  • h(x) = sin(x) (Trigonometric function)