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The notation y = f (x) y = f (x) defines a function named f. f. This is read as “ y “ y is a function of x. ” x. ” The letter x x represents the input value, or independent variable. The letter y, y, or f (x), f (x), represents the output value, or dependent variable.
The f is just a way for you to know that when you see f(x) to treat it as a function and not mistakenly treat it as multiplying one variable by the other (it DOES NOT mean f multiplied by x). It does not have to be an f, it can be any symbol and using different symbols such as h(a) helps differentiate one function from another.
In f (x), the f is the name used to identify the given function, while the x is the argument of the function, and describes the input value of the function. The argument of the function must be the same as the variable used on the right side of the equation.
The most common graphs name the input value \(x\) and the output \(y\), and we say \(y\) is a function of \(x\), or \(y=f(x)\) when the function is named \(f\). The graph of the function is the set of all points \((x,y)\) in the plane that satisfies the equation \(y=f(x)\).
The function f´(x), which would be read ``f-prime of x'', means the derivative of f(x) with respect to x. If we say y = f(x), then y´ (read ``y-prime'') = f´(x). This is even sometimes taken as far as to write things such as, for y = x 4 + 3. x (for example), y´ = (x 4 + 3x)´.
A special relationship where each input has a single output. It is often written as "f (x)" where x is the input value, but can be in other forms. Example: f (x) = x/2. In words: "f of x equals x divided by 2". It is a function because each input "x" has a single output "x/2": • f (2) = 1. • f (16) = 8.
A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input. Input, Relationship, Output. We will see many ways to think about functions, but there are always three main parts: The input. The relationship. The output.
Lagrange's notation. In Lagrange's notation, the derivative of f is expressed as f ′ (pronounced "f prime" ). This notation is probably the most common when dealing with functions with a single variable. If, instead of a function, we have an equation like y = f ( x) , we can also write y ′ to represent the derivative.
A function is an equation for which any x that can be put into the equation will produce exactly one output such as y out of the equation. It is represented as; y = f (x) Where x is an independent variable and y is a dependent variable.
Sep 12, 2011 · What is f(x)? It is a different way of writing "y" in equations, but it's much more useful!
