Functions, Domains, Ranges, and Graphs

Install and import#

npm install fintech-algorithms

import { functionsDomainsRangesAndGraphs } from "fintech-algorithms/foundations/mathematical-language-and-quantitative-reasoning/functions-domains-ranges-and-graphs";

Signature#

functionsDomainsRangesAndGraphs(input)

Evaluates the straight-line function intercept + slope * value at every entry of values and reports the input span it was evaluated over alongside the output span it produced.

Parameters#

Returns#

{ domain: [number, number]; range: [number, number]; outputs: number[] }

domain is the smallest and largest entry of values, range the smallest and largest of the computed outputs, and outputs the value of the function at each input, in input order.

Errors#

• When input is not a plain object — throws TypeError
• When values is missing, empty, or not an array — throws RangeError
• When values contains a value that is not a finite number — throws RangeError

Complexity: time O(n), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

{
  "values": [1, 2, 3, 4, 5],
  "startingCash": 1000,
  "inflows": 250,
  "outflows": 120,
  "slope": 2,
  "intercept": 1,
  "part": 25,
  "whole": 200,
  "elapsed": 5,
  "old": 4.5,
  "new": 4.75,
  "base": 16,
  "exponent": 0.5,
  "a": 2
}

Showing 14 of 28 fields.

Call#

functionsDomainsRangesAndGraphs(input)

Returns#

object with 2 fields: domain, range

{
  "domain": [1, 5],
  "range": [3, 11]
}

Diagrams#

Calculation flow#

flowchart LR
    A["Name the input"] --> B["Apply: fee(amount) = fixed fee + (rate / 100) × amount"]
    B --> C["Check units and boundary"]
    C --> D["Explain the output"]

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• College Algebra: Domain and Range — OpenStax
• NIST/SEMATECH e-Handbook of Statistical Methods — NIST/SEMATECH
• Author-derived and synthetic boundary

The rest of the Mathematical Language and Quantitative Reasoning family#

• Variables, Constants, Expressions, and EquationsSubstitutes named quantities into a cash-balance equation and checks that the rearranged form still holds, returning the ending…
• Ratios, Proportions, Rates, and PercentagesTurns a part-and-whole pair into a ratio and a percentage, and turns the same part spread over an elapsed span into a rate per …
• Percentage Change, Percentage Points, and Basis PointsExpresses the move from an old level to a new one three ways: as a percent change relative to the old level, as a raw differenc…
• Exponents, Roots, and LogarithmsApplies the three operations that share one base: raising it to an exponent, taking its square root, and taking its natural log…
• Summation, Products, and Index NotationReduces a series to its sum and its product, and re-emits it as explicitly numbered terms so subscript notation can be read aga…
• Linear Equations and SystemsSolves the two-equation system a*x + b*y = c and d*x + e*y = f by Cramer's rule, returning the solution and the determinant…
• Inequalities, Bounds, and ConstraintsTests a candidate number against a lower and upper bound, reporting whether it is admissible, what it becomes once clamped into…
• Units, Dimensions, Scale, and NormalizationRescales a series by subtracting an offset and dividing by a scale, so numbers recorded in one unit can be compared on a common…
• Rounding, Precision, Tolerance, and Significant DigitsRounds a candidate to a fixed number of decimal places and measures it against a reference value and an allowed tolerance.