Function Table in Math (original) (raw)
Last Updated : 23 Mar, 2026
A function table is used to organize and display the relationship between inputs (often called _x values or independent variables) and their corresponding outputs (often called _y values or dependent variables) in a function. It shows how a specific function transforms one value (input) into another (output).
**Here's how it works:
- Input (x): These are the values that we plug into the function.
- Output (y): These are the results you obtain after applying the function to the input values.
**Example: Consider the function y = 2x + 3. The function table is
| x (Input) | y (Output) |
|---|---|
| 0 | 3 |
| 1 | 5 |
| 2 | 7 |
| 3 | 9 |
| 4 | 11 |
In this example, for every input x, the output y is calculated by doubling x and adding 3.
Creating a Function Table
- **Step 1: Choose Input Values
For the function f(x) = 3x − 4, let the values of x be:
**x = − 2, − 1, 0, 1, 2
- **Step 2: Calculate Output Values
Now, plug each chosen x value into the function to determine the corresponding f(x) (output):
- f(−2) = 3(−2) − 4 = −10
- f(−1) = 3(-1) - 4 = -7
- f(0) = 3(0) − 4 = −4
- f(1) = 3(1) − 4 = −1
- f(2) = 3(2) − 4 = 2
- **Step 3: Create The Table
Finally, organize the input and output data in a table format:
| Input (x) | Output (f(x)) |
|---|---|
| -2 | -10 |
| -1 | -7 |
| 0 | -4 |
| 1 | -1 |
| 2 | 2 |
Function Tables for Various Functions
Linear Functions
Linear functions are best described by a straight line and follow the general form y = mx + b, where m is the slope and b is the y-intercept. Since the output and input are linearly dependent, filling the function table is simple.
Consider the linear function f(x) = 2x + 1. The function table for this linear function is
| x (Input) | f(x) = 2x + 1 (Output) |
|---|---|
| 0 | 1 |
| 1 | 3 |
| 2 | 5 |
| 3 | 7 |
| 4 | 9 |
Quadratic Functions
Quadratic functions follow the general form y = ax² + bx + c and are represented by a parabolic curve. Since the output depends on the square of the input, the rate of change is not constant, but creating a function table remains straightforward.
Consider the quadratic function f(x) = x² + 2x + 1. The function table for this quadratic function is
| _x (Input) | f(x) = x2 + 2x + 1 (Output) |
|---|---|
| -2 | 1 |
| -1 | 0 |
| 0 | 1 |
| 1 | 4 |
| 2 | 9 |
Polynomial Functions
Polynomial functions are expressions made by adding terms where a variable is raised to different powers and multiplied by coefficients, such as y = ax2 + bx + c, y = x5 - 3, etc.
Consider the polynomial function f(x) = 2x3 − 3x2 + x − 5. The function table for this polynomial function is
| _x (Input) | f(x) = 2x3 − 3x2 + x − 5 (Output) |
|---|---|
| -2 | -35 |
| -1 | -11 |
| 0 | -5 |
| 1 | -5 |
| 2 | 5 |
Rational Functions
Rational functions are of the type y = p(x) / q(x), where both p(x) and q(x) are polynomials. The output depends upon the input and can be very large, especially when the denominator is close to zero.
Consider the rational function: f(x) = \frac{2x + 1}{x - 1}
This function is defined for all real values of x except x = 1, where the denominator becomes zero.
| _x (Input) | f(x) = (2x + 1)/(x − 1) (Output) |
|---|---|
| -2 | -1/3 |
| -1 | 1/2 |
| 0 | -1 |
| 2 | 5 |
| 3 | 7/2 |
Interpreting Function Tables
- **Check for consistency: Verify that each output is properly calculated from its corresponding input values.
- **Identify patterns: Search for trends of how the output is affected as the inputs increase or decrease.
- **Determine the function rule: Use the input-output pairs to identify the function’s rule or pattern.
Related Articles
Solved Examples
**Example 1: Create a function table for the linear function y = 3x − 2 using the input values x = − 1, 0, 1, 2, 3.
**Solution:
- For x = − 1, y = 3( − 1) − 2 = − 3 − 2 = − 5
- For x = 0, y = 3(0) − 2 = 0 − 2 = − 2
- For x = 1, y = 3(1) − 2 = 3 − 2 = 1
- For x = 2, y = 3(2) − 2 = 6 − 2 = 4
- For x = 3, y = 3(3) − 2 = 9 − 2 = 7
Thus, Function table for y = 3x − 2 is:
x y = 3x − 2 -1 -5 0 -2 1 1 2 4 3 7
**Example 2: Fill in the missing values in the function table for y = x2 + 2x given x = − −2, −1, 0, 1, 2.
**Solution:
For x = − 2, y = ( − 2)2 + 2( − 2) = 4 − 4 = 0
- For x = − 1, y = ( − 1)2 + 2( − 1) = 1 − 2 = − 1
- For x = 0, y = 02 + 2(0) = 0
- For x = 1, y = 12 + 2(1) = 1 + 2 = 3
- For x = 2, y = 22 + 2(2) = 4 + 4 = 8
Thus, Function table for y = x2 + 2x is:
x y = x2 + 2x -2 0 -1 -1 0 0 1 3 2 8
**Example 3: What is the output of the function y = 2x + 1 when the input is 5?
**Solution:
Putting x = 5, y = 2(5) + 1 = 10 + 1 = 11.
Practice Problems
**Problem 1: Create a function table for y = 4x + 1.
**Problem 2: Create a function table for y = x3 − x.
**Problem 3: What is the output of the function y = 2x + 5 when the input is x = 4?
**Problem 4: Create a function table for y = x2 + 2x + 1 using x = − −2, −1, 0, 1, 2.
**Problem 5: Create a function table for y = 5x − 3 using x = − 3, − 1, 0, 1, 3.
**Problem 6: Create a function table for y = − x + 4 using x = − 3, − 2, 0, 2, 3.
**Problem 7: Create a Function Table for y = 3x / 2 − 1 using x = − 2, − 1, 0, 1, 2.