Function Table in Math

A function table in math is a table 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. The table 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 get after applying the function to the input values.

Example

Consider the function y = 2x + 3. The function table for this equation might look like this:

In this example, for every input x, the output y is calculated by doubling x and adding 3.

How to Create a Function Table?

Creating a function table involves a few simple steps:

• Step 1: Identify the Function

First, you need to know the function you're working with. For example, let's say the function is:

f(x) = 3x − 4

This means, that for any given value of x, you'll multiply it by 3 and then subtract 4 to get the output.

• Step 2: Choose Input Values

The choice of inputs can be in terms of its relation to the problem or in terms of the behavior of the function. It is necessary to take into account positive and negative values as well as zero to get a definite picture of the function.

For example, let the values of x be:

x = − 2, − 1, 0, 1, 2

• Step 3: Calculate Output Values

Now, plug each chosen x value into the function to find the corresponding f(x) (output). Using our function f(x) = 3x − 4, we'll calculate:

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

• Step 4: Create the table

Finally, organize the input and output data in a table format, which usually consists of two columns: On the input values for one relationship holds Thus for input values the one-to-one relationship is the existing again. (x) and another for the output values f(x).

Function Tables for Various Functions

Function Table for some common functions are discussed as follows:

Linear Functions

Linear functions are best described by a straight line as depicted in the following equation; y = mx + b, where m is the slope and b is the y-intercept. The dependent variable is directly related to the independent variable hence filling the function table does not pose any difficulty.

Consider the linear function: f(x) = 2x + 1

This function takes an input x, multiplies it by 2, and then adds 1 to get the output. Function Table for this linear function is:

Quadratic Functions

Parabolic functions are quadratic in nature and have the following general form y = ax² + bx + c. The output increases in proportion with the square of the input which is reflected by a parabolic curve in the function table.

Consider the quadratic function: f(x) = x² + 2x + 1

This function takes an input x, squares it, adds twice the input, and then adds 1 to get the output. Function Table for this quadratic function is:

Polynomial Functions

For polynomial functions there are terms combined with coefficients raised to the powers of fixed value, here in the equation there are terms with powers varying as; ^3, ^2, and ^1. g. , y = ax² + bx + c. Four-parameter quadratic equation of the form y = 2x² + 5x + 3, and each of the terms having different powers of x.

Consider the polynomial function: f(x) = 2x³ − 3x² + x − 5

This function takes an input x and applies the polynomial rule to calculate the output. 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: f(x) = \frac{2x + 1}{x - 1}

This function takes an input x, applies the rational function rule, and gives an output, except where the denominator is zero (i.e., x = 1, where the function is undefined).

How to Interpret Function Tables?

To interpret a function table:

• Check for consistency: Make sure the output of the figures is properly computed depending on the input values.
• Identify patterns: Search for trends of how the output is affected as the input is either raised or lowered.
• Understand the function rule: Therefore, you should use the table below to check and appreciate the rule governing the function.

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:

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:

Example 3: What is the output of the function y = 2x + 1 when the input is 5?

Solution:

Plugging in x = 5 into the function: y = 2(5) + 1 = 10 + 1 = 11.

Practice Problems on Function Tables

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.

Read More,

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