{
  "id": "function-table",
  "version": "7be004a480c1",
  "status": "published",
  "name": "Function Table Calculator",
  "question": "What is the function table?",
  "summary": "Makes an input-output table of a function y = f(x) from a start value to an end value in equal steps, and draws its graph.",
  "category": "math",
  "subcategory": "algebra",
  "url": "https://www.acalculator.org/math/function-table-calculator",
  "markdown": "https://www.acalculator.org/math/function-table-calculator.md",
  "kind": "function",
  "method": "x₀ = start, xₖ = start + k × step for k = 0, 1, 2, … while xₖ ≤ end; each row is (xₖ, f(xₖ)).",
  "assumptions": [
    "A row where f has no real value (the square root or logarithm of a negative number, a division by zero) shows “undefined”.",
    "The table has at most 51 rows."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "f": {
        "title": "Function f(x)",
        "description": "The rule, typed like x^2 + 3x - 4, 2x + 1, sqrt(x) or sin(x).",
        "type": "string",
        "maxLength": 200
      },
      "from": {
        "title": "Start x",
        "description": "The first x in the table.",
        "type": "number",
        "minimum": -1000000,
        "maximum": 1000000
      },
      "to": {
        "title": "End x",
        "description": "The last x in the table (the table stops at or before it).",
        "type": "number",
        "minimum": -1000000,
        "maximum": 1000000
      },
      "step": {
        "title": "Step",
        "description": "How much x goes up from one row to the next.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      }
    }
  },
  "outputs": {
    "values": {
      "label": "f(x) values",
      "description": "The outputs f(x) in order, each to 10 significant figures; “undefined” where f has no value.",
      "format": "text"
    },
    "table": {
      "label": "Table",
      "description": "Each row as x → f(x), separated by semicolons.",
      "format": "text"
    },
    "rows": {
      "label": "Rows",
      "description": "How many x values the table has.",
      "format": "integer"
    },
    "min": {
      "label": "Smallest f(x)",
      "description": "The smallest output in the table.",
      "format": "number"
    },
    "max": {
      "label": "Largest f(x)",
      "description": "The largest output in the table.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "f": "x^2 + 3x - 4",
      "from": -2,
      "to": 2,
      "step": 1
    },
    "outputs": {
      "values": "-6, -6, -4, 0, 6",
      "table": "x = -2 → f(x) = -6; x = -1 → f(x) = -6; x = 0 → f(x) = -4; x = 1 → f(x) = 0; x = 2 → f(x) = 6",
      "rows": 5,
      "min": -6,
      "max": 6
    },
    "text": "f(x) = x^2 + 3x - 4 from x = -2 to 2 gives -6, -6, -4, 0, 6."
  },
  "examples": [
    {
      "given": {
        "f": "x^2 + 3x - 4",
        "from": -2,
        "to": 2,
        "step": 1
      },
      "expect": {
        "values": "-6, -6, -4, 0, 6",
        "rows": 5,
        "min": -6,
        "max": 6
      },
      "source": "OpenStax, Algebra and Trigonometry 2e, §3.1 Functions and Function Notation (evaluating a function given by a formula, input-output tables), https://openstax.org/books/algebra-and-trigonometry-2e/pages/3-1-functions-and-function-notation (Example 6: f(2) = 4 + 6 − 4 = 6); hand calculation in content.mdx for the other rows"
    },
    {
      "given": {
        "f": "2x + 1",
        "from": 0,
        "to": 1,
        "step": 0.25
      },
      "expect": {
        "values": "1, 1.5, 2, 2.5, 3",
        "table": "x = 0 → f(x) = 1; x = 0.25 → f(x) = 1.5; x = 0.5 → f(x) = 2; x = 0.75 → f(x) = 2.5; x = 1 → f(x) = 3"
      },
      "source": "hand calculation in content.mdx: 2 × 0.25 + 1 = 1.5, and so on; OpenStax, Algebra and Trigonometry 2e, §3.1 Functions and Function Notation (evaluating a function given by a formula, input-output tables), https://openstax.org/books/algebra-and-trigonometry-2e/pages/3-1-functions-and-function-notation"
    },
    {
      "given": {
        "f": "sqrt(x)",
        "from": -1,
        "to": 4,
        "step": 1
      },
      "expect": {
        "values": "undefined, 0, 1, 1.414213562, 1.732050808, 2",
        "rows": 6,
        "min": 0,
        "max": 2
      },
      "source": "hand calculation in content.mdx: √0 = 0, √2 = 1.414213562, √3 = 1.732050808, √4 = 2; OpenStax, Algebra and Trigonometry 2e, §3.1 Functions and Function Notation (evaluating a function given by a formula, input-output tables), https://openstax.org/books/algebra-and-trigonometry-2e/pages/3-1-functions-and-function-notation (domain of a function)"
    },
    {
      "given": {
        "f": "x/10",
        "from": 0,
        "to": 0.3,
        "step": 0.1
      },
      "expect": {
        "values": "0, 0.01, 0.02, 0.03",
        "rows": 4
      },
      "source": "hand calculation in content.mdx: (0.3 − 0) ÷ 0.1 = 3 steps, so 4 rows; OpenStax, Algebra and Trigonometry 2e, §3.1 Functions and Function Notation (evaluating a function given by a formula, input-output tables), https://openstax.org/books/algebra-and-trigonometry-2e/pages/3-1-functions-and-function-notation"
    }
  ],
  "sources": [
    "OpenStax, Algebra and Trigonometry 2e, §3.1 Functions and Function Notation: functions as input-output rules, evaluating a function given by a formula (Example 6: f(x) = x² + 3x − 4, f(2) = 6), tables of values and domains. https://openstax.org/books/algebra-and-trigonometry-2e/pages/3-1-functions-and-function-notation (retrieved 2026-10-02)"
  ],
  "related": [
    "inverse-function",
    "slope",
    "equation-solver",
    "polynomial"
  ],
  "changelog": []
}