# Mathematical function graphs

## Would you like to graph different types of functions and study their behavior?

The online mathematical function graphs simulations on this page will allow you to graphically visualize different functions and see how the graphs change as you alter any of their parameters.

The online mathematical function graphs simulations on this page will allow you to graphically visualize different functions and see how the graphs change as you alter any of their parameters.

The graphing of functions is a powerful tool in mathematics that allows you to visualize and understand the behavior of a relationship between two variables. A function is a rule that associates to each element of a set called domain a single element of another set called range.

The graphical representation of a function is made on a Cartesian coordinate system, which consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). The x-axis represents the domain of the function, while the y-axis represents the range.

To graph a function, values are assigned to the independent variable (x) and the corresponding values of the dependent variable (y) are calculated according to the function rule. These points (x, y) are plotted on the Cartesian plane and joined by a continuous line or a smooth curve. The set of all these points forms the graph of the function.

The graph of a function can have several characteristics, such as slope, concavity, points of intersection with the axes, as well as horizontal or vertical asymptotes. These features provide valuable information about the behavior of the function.

By analyzing the graph of a function, properties such as growth or decay of the function, maxima and minima, inflection points and symmetry can be determined. In addition, the graphical representation allows the visualization of patterns, trends and relationships between variables, which facilitates the interpretation of the results.

The graphical representation of functions is widely used in various areas, such as physics, economics, engineering and biology. It helps to model phenomena, predict behavior and make decisions based on data.

Current technology, such as computer plotting programs and graphing calculators, greatly facilitates the graphing of functions. These tools allow accurate and detailed graphing of complex functions, which helps to explore and better understand their behavior.

**Below are several simulations and other educational resources, which can also serve as very illustrative examples. In addition, a selection of books and courses is included to help you broaden your knowledge of this subject.**

- Slope
- Quadratic

## Graphing slope-intercept

Explore the world of lines. Investigate the relationships between linear equations, slope, and line graphs. Test yourself in the line game!

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## Graphing quadratic functions

Discover how changing the coefficients changes the shape of a curve. View graphs of individual terms (e.g., y = bx) to see how they add up to generate the polynomial curve. Generate definitions for vertex, roots, and axis of symmetry. Compare different forms of a quadratic function. Define a curve by its focus and directrix.

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###### Mathematics

MathTrackX: Polynomials, Functions and Graphs

###### Algebra

Linear Algebra I: Linear Equations