Intercepts of Graph

intercept_points(equation_type, coefficients, precision=4)

Calculates the roots of a specific function

Parameters

• equation_type (str) – Name of the type of function for which intercepts must be determined (e.g., ‘linear’, ‘quadratic’)

• coefficients (list of int or float) – Coefficients to use to generate the equation to investigate

• precision (int, default=4) – Maximum number of digits that can appear after the decimal place of the results

Raises

• ValueError – First argument must be either ‘linear’, ‘quadratic’, ‘cubic’, ‘hyperbolic’, ‘exponential’, ‘logarithmic’, ‘logistic’, or ‘sinusoidal’

• TypeError – Second argument must be a 1-dimensional list containing elements that are integers or floats

• ValueError – Last argument must be a positive integer

Returns

points – Values of the x-coordinates at which the original function crosses the x-axis; if the function is sinusoidal, then only the initial results within a four-period interval will be listed, but general forms will also be included; if the function has no x-intercepts, then it will return a list of None

Return type

list of float or str

See also

• Roots for key functions: linear_roots(), quadratic_roots(), cubic_roots(), hyperbolic_roots(), exponential_roots(), logarithmic_roots(), logistic_roots(), sinusoidal_roots()

• Graphical analysis: critical_points(), sign_chart(), key_coordinates()

Notes

• Domain of a function: \(x_i = \{ x_1, x_2, \cdots, x_n \}\)

• X-intercepts (roots) of the function: \(x_r = \{ r \mid r \in x_i, f(r) = 0 \}\)

• Intercepts

Examples

Import intercept_points function from regressions library

>>> from regressions.analyses.intercepts import intercept_points

Calculate the roots of a cubic function with coefficients 1, -15, 66, and -80

>>> points_cubic = intercept_points('cubic', [1, -15, 66, -80])
>>> print(points_cubic)
[2.0, 5.0, 8.0]

Calculate the roots of a sinusoidal function with coefficients 3, 1, -2, and 3

>>> points_sinusoidal = intercept_points('sinusoidal', [3, 1, -2, 3])
>>> print(points_sinusoidal)
[-3.5708, 2.7124, 8.9956, 15.2788, 21.5619, '-3.5708 + 6.2832k']