# What is the function table?

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.

- Page: https://www.acalculator.org/math/function-table-calculator
- JSON spec: https://www.acalculator.org/math/function-table-calculator.json
- Version: 7be004a480c1

## Default answer

Example with the default inputs (Function f(x) x^2 + 3x - 4, Start x -2, End x 2, Step 1): f(x) = x^2 + 3x - 4 from x = -2 to 2 gives -6, -6, -4, 0, 6.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| f | Function f(x) | The rule, typed like x^2 + 3x - 4, 2x + 1, sqrt(x) or sin(x). |
| from | Start x | The first x in the table. |
| to | End x | The last x in the table (the table stops at or before it). |
| step | Step | How much x goes up from one row to the next. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| values | f(x) values | The outputs f(x) in order, each to 10 significant figures; “undefined” where f has no value. |
| table | Table | Each row as x → f(x), separated by semicolons. |
| rows | Rows | How many x values the table has. |
| min | Smallest f(x) | The smallest output in the table. |
| max | Largest f(x) | The largest output in the table. |

## 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.

## Worked examples

1. f = x^2 + 3x - 4, from = -2, to = 2, step = 1 gives 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).
2. f = 2x + 1, from = 0, to = 1, step = 0.25 gives 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: 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.
3. f = sqrt(x), from = -1, to = 4, step = 1 gives values = undefined, 0, 1, 1.414213562, 1.732050808, 2, rows = 6, min = 0, max = 2. 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 (domain of a function).
4. f = x/10, from = 0, to = 0.3, step = 0.1 gives values = 0, 0.01, 0.02, 0.03, rows = 4. 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.

## FAQ

### What is a function table?

A table of inputs and outputs. Each row holds one x and the value f(x) that the rule gives for it. For f(x) = x² + 3x − 4, the row for x = 2 holds 4 + 6 − 4 = 6.

### How do I make a table of values for a function?

Pick the x values, usually a start, an end and a fixed step, and put each one into the rule. From −2 to 2 in steps of 1, f(x) = x² + 3x − 4 gives −6, −6, −4, 0 and 6.

### How do I type the function?

Use x as the variable, + − * / and ^ for powers, and brackets. 3x means 3 × x. Functions include sqrt, ln (log is also the natural log), log10, sin, cos, tan, and |x| for the absolute value; pi and e are the constants.

### Why does a row say undefined?

The function has no real value at that x: a square root or logarithm of a negative number, or a division by zero. sqrt(x) at x = −1 is undefined, so that row shows the word instead of a number.

### Does the table always reach the end value?

Only if a whole number of steps fits. The table stops at the last x that is not past the end. From 0 to 1 in steps of 0.3 the rows are 0, 0.3, 0.6 and 0.9.

### Are trig functions in degrees or radians?

In radians, as in most algebra and calculus books. sin(pi/2) is 1. To use degrees, multiply by pi/180: sin(x*pi/180).

## 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)