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Function Plotter

This calculator graphs a user-specified function on a cartesian plane. It also tabulates the x and y values in a specified range.


Calculation

Inputs



Function
:x**sin(x/2)​



Minimum x-value
:-10.00​



Maximum x-value
:10.00​



Number of points
:100​


📝 Guide on function notation

The "Function" input parameter must use Python notation, see below.


Output

Graph

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Explanation

What is a function?

A function establishes that for each value of x, there is a corresponding value of y under an explicit rule or formula. We can say, by definition, that "y is a function of x". Mathematically this is written as:

y=f(x)y = f(x)
This calculator's inputs can be mathematically expressed as:

y=f(x)=[function] ,[min. value]≤x≤[max. value]y=f(x)=[\text{function}]\ , [\text{min.\ value}] \le x \le [\text{max.\ value}]
Where:
  1. Function is the equation y as a function of x. Use Python notation in this calculator
  2. Minimum x-value is the minimum value of x in it's range
  3. Maximum x-value is the maximum value of x in it's range
  4. Number of points is the number of points to be plotted

What is the cartesian coordinate plane?

The cartesian coordinate plane is a 2-dimensional area with two perpendicular numbered axes to specify a location. The horizontal line is called the "x-axis", while the vertical line is called the "y-axis". An x-value and a y-value can describe a location

, also called a "point". The intersection of these two axes is called the "origin", where both x and y are equal to zero. The coordinate axes divide the plane into four regions called quadrants.
Cartesian coordinate plane, showing the x & y sign convention in each of the four quadrants


Common Types of Functions

Discover common types of functions in the toggles below.

Linear Function

Linear functions are a straight line. The formula is in the form of:

y=mx+by = mx+b
Where:
  1. 
    
    is a constant, and defines the slope of the line
  2. 
    
    is a constant, and defines the y-intercept of the line
Example of a linear function


Quadratic Function

Quadratic functions graph a parabola, The formula is given by:

y=ax2+bx+cy=ax^2+bx+c
Where:
  1. 
    
    and
    
    are constants
The parabola opens upward or downward depending on if the parameter

is positive or negative, respectively.
Example of a quadratic function


Power Function

Polynomial Function

Exponential Function

Logarithmic Function

Sinusoidal Function



Related Resources

  1. 🔗 Polar-Cartesian Coordinate Converter
  2. 🔗 Poisson Distribution Calculator
Check out our full library of CalcTree templates here!



References

  1. AMSI (2013). Functions I - A guide for teachers (Year 11 - 12). Education Services Australia. Available at: https://amsi.org.au/ESA_Senior_Years/PDF/Functions12b.pdf
  2. AMSI (2013). Functions II - A guide for teachers (Year 11 - 12). Education Services Australia. Available at: https://amsi.org.au/ESA_Senior_Years/PDF/Functions22c.pdf
  3. Hoib, E. (2018). The Algebra Help e-Book. Section 5.2. Available at: https://openbooks.library.umass.edu/p132-lab-manual/chapter/review-of-the-types-of-graphs/