Function Table in Math

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

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):

1. f(−2) = 3(−2) − 4 = −10
2. f(−1) = 3(-1) - 4 = -7
3. f(0) = 3(0) − 4 = −4
4. f(1) = 3(1) − 4 = −1
5. f(2) = 3(2) − 4 = 2

• Step 3: Create The Table

Finally, organize the input and output data in a table format:

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

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

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

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:

This function is defined for all real values of x except x = 1, where the denominator becomes zero.

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

• What is a Function?
• Types of Functions
• Domain and Range
• Invertible Functions

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.