Introduction

A function is a rule that takes in and works on an input and gives an output. It is usually represented as fx = y, where x is the input variable and y is the output variable.

By giving different whole number values to x, values of y can be found from the function rule. The x and y values are put in a table and then plotted as a graph.

Plotting a graph

So, from a function rule, x and y values can found and put in a table and also plotted as a graph.

Conversely, from a graph we can find x and y values and make a table of those values and find the function rule for the given graph also.

Example 1

The table below describes a function. Graph this function.

Inputx	Outputy
0	0
2	4
4	8
6	12
8	16

Solution

Step 1:

From the table, we get the coordinates of the points as 0,0, 2,4, 4,8, 6,12, and 8,16

Step 2:

Making a plot of these points, we get

Example 2

The graph of a function is given below. Fill in the table for this function.

Solution

Step 1:

From the graph plot, we get the coordinates of the points as 0,0, 1,4, 2,9, 3,5, and 4,10

Step 2:

Making a table of the x and y values, we get

Inputx	Outputy
0	0
1	4
2	9
3	5
4	10

Definition

Unit rate is defined as a ratio in which denominator is 1. In general, a unit rate is the number of dependent variables per one independent variable.

For example − A monkey eats 8 bananas in 2 minutes

The unit rate here is the number of bananas the monkey eats in a minute.

Unit rate = 8/2 = 4 bananas per minute.

Unit rate and table

If we have a proportional relationship like for example 9for3kg,wecanmakeatableofvaluesandgraphtherelationship.Wealreadyhavelearntaboutunitrate.Inthiscasetheunitrateisthenumberofdollarsper1kg.Heretheunitrateisfoundas9/3kg = $3/kg.

In a table or graph, representing proportional relationships, the constant of proportionality and the unit rate are same.

Given a unit rate we can write pairs of x and y values following the proportional relationship as follows. For example if the unit rate is 3/kgwecanwrite(1kg,3), 2kg,$6, 3kg,$9, 4kg,$12, 5kg,$15 and so on. We then put these ordered pairs in a table as follows.

Weight in kgx	Cost in $(y)
1	3
2	6
3	9
4	12
5	15

Unit rate and graph

The proportional relationship for given rate $3/kg can be written as an equation y = 3x. The same can be plotted as a graph given below.

Given a unit rate, we can write a function rule like y = mx, where m is the unit rate, x and y are the variables. Using this rule we can find points with x and y values which can be put in a table. Then we plot these points on a graph.

Example 1

The relationship having unit rate is given by the equation: y = 2x + 1 Make a table and plot 5 points.

Solution

Step 1:

In the equation y = 2x + 1,

For x = 0, y = 1, for x = 1, y = 3 and so on

For different values of x, we get the following table

Inputx	Outputy
0	1
1	3
2	5
3	7
4	9

Step 2:

Plotting these points we get this graph

Example 2

The relationship having unit rate is given by the equation: y = 5x. Make a table and plot 5 points.

Solution

Step 1:

In the equation y = 5x

For x = 0, y = 0, for x = 1, y = 5 and so on

For different values of x, we get the following table

Inputx	Outputy
0	0
1	5
2	10
3	15
4	20

Step 2:

Plotting these points we get this graph

This tutorial provides comprehensive coverage of Tables, Graphs, Functions and Sequences based on Common Core CCSS and State Standards and its prerequisites. Students can navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs. This simple tutorial uses appropriate examples to help you understand Tables, Graphs, Functions and Sequences in a general and quick way.

Audience

This tutorial has been prepared for beginners to help them understand the basics of Tables, Graphs, Functions and Sequences. After completing this tutorial, you will find yourself at a moderate level of expertise in Tables, Graphs, Functions and Sequences, from where you can advance further.

Prerequisites

Before proceeding with this tutorial, you need a basic knowledge of elementary math concepts such as number sense, basic arithmetic operations, whole numbers, fractions, decimals, algebraic equations, unit rate, coordinate plane, tables, graphs, and so on.