Function Calculator

The Function Calculator is a tool that allows you to many properties of functions. Easily explore functions by examining their parity, domain, range, intercepts, critical points, intervals of increase/decrease, local and global extrema, concavity intervals, inflection points, derivatives, integrals, asymptotes, and so on.

How to Use the Function Calculator?

• Input

  Enter the function you want to analyze. If necessary, enter the interval which you are interested in.

• Calculation

  Click the "Calculate" button to start the process.

• Result

  The calculator will quickly display the properties of the function.

What Is a Function?

In mathematics, a function is a formula that, for every value from the input set (domain), produces some value. The set of such values forms the output set (range, codomain). The function is called one-to-one if no two elements from its domain give the same element from the range.

Functions are typically denoted using various notations. The most common notation is $$$f(x)$$$. In the notation $$$f(x)$$$ $$$f$$$ is the function symbol and $$$x$$$ represents the input variable.

For example, $$$f(x)=x^2$$$ is a quadratic function. If $$$x=-2$$$, then $$$f(-2)=(-2)^2=4$$$. If $$$x=2$$$, then $$$f(2)=2^2=4$$$. By the way, it is not one-to-one, since there are two elements, namely $$$-2$$$ and $$$2$$$, that give $$$4$$$.

What Are the Components of a Function?

• Domain: The domain of a function is the set of all possible input values. It defines where the function is defined or valid.
• Codomain: The codomain of a function is the set of all possible output values. It represents the values that the function can produce.
• Range: The range of a function is the set of all actual output values. It represents the values that the function actually produces.
• Input: The input of a function is the value of its variable you provide as an argument to the function. It's the value for which you want to determine the corresponding output.
• Output: The output of a function is the result of applying the function to the input value(s). It represents the dependent variable's value corresponding to the given input.

What Is the Mathematical Expression of a Function?

A function is often expressed using a formula or rule that describes how the input values are transformed into output values. This formula can be very simple, for example, $$$f(x)=x$$$, or very complex, for example, $$$f(x,y,z)=\frac{x^2+y^2z}{z-xy}$$$ (a multivariable function). Here are some examples:

• Linear Function. A linear function has the following form:

  $$f(x)=mx+b$$

  Example: $$$f(x)=2x+3$$$.

  This function represents a straight line on a graph, where $$$m$$$ is the slope, and $$$b$$$ is the y-intercept.

• Quadratic Function. A quadratic function has the following form:

  $$f(x)=ax^2+bx+c$$

  Example: $$$f(x)=3x^2-4x+1$$$.

  This function represents a parabolic curve.

• Exponential Function. An exponential function has the following form:

  $$f(x)=a\cdot b^x$$

  Example: $$$f(x)=2\cdot3^x$$$.

  This function exhibits exponential growth or decay.

Why Choose Our Function Calculator?

• Ease of Use

  Our calculator is designed with user-friendliness in mind. It features an intuitive interface that allows both beginners and experts to navigate with ease.

• Versatility

  Our calculator can handle a wide range of functions to meet your requirements.

• Accurate Results

  Our calculator provides accurate results. You can trust it.

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