Ways to represent a function

🏆Practice function representation

Ways to represent a function

Algebraic Representation

Representation using an equation of XX and YY

Graphical representation

Representation using a graph, plotting on the XX and YY axis

Tabular representation

Representation using a table X,YX,Y representing points on the graph

Verbal representation

Expressing the relationship between XX and YY using words

Function notation

Y=Y= or f(x)=f(x)=

Start practice

Test yourself on function representation!

einstein

Is the given graph a function?

–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–4–4–4–3–3–3–2–2–2–1–1–1111222333000

Practice more now

Ways to represent a function

Algebraic representation of a function

Before we talk about algebraic representation, it is important to understand what a function means.
A function describes the relationship between XX and YY.
In any function, XX is the independent variable and YY is the dependent variable. This means that every time we change XX, we get a different YY.
Y depends on XX and XX depends on nothing.

Important point: For each XX there will be only one YY!

An algebraic representation of a function is essentially the equation of the function.

Let's look at some examples of algebraic representation of a function and analyze them:
Y=X3Y=X-3

In this equation, it is clear that YY depends on the XX we substitute into the equation.
If X=1X=1, then Y=2Y=-2
If X=0X=0, then Y=3Y=-3
If X=2X=2, then Y=1Y=-1
In other words, the relationship between XX and YY is that YY will always be 33 less than XX.

Now let's examine another equation:
y=2x5y=2x-5

Also in this equation, it is clear that YY depends on the XX we substitute into the equation.
If X=3X=3, then Y=1Y=1
If X=4X=4, then Y=3Y=3
If X=5X=5, then Y=5Y=-5
In this equation, it is difficult to define in words the relationship between XX and YY, so we will say that the relationship between them is the equation itself:
y=2x5y=2x-5

Now let's examine another equation:
y=xy=x

In this equation, it is also clear that YY depends on the XX we substitute into the equation.
If X=3X=3, then Y=3Y=3
If X=2X=2, then Y=2Y=2
If X=1X=1, then Y=1Y=1
The relationship between XX and YY is that they are identical each time.

Click here to learn more about the algebraic representation of a function!

Graphical representation of a function

A graphical representation of a function shows us how the function looks on the XX and YY axes.
What is most important to know?
For each XX, there is only one YY, and to draw a function as a graph, it is advisable to find at least 3 points of the function.
How to draw the function:
Each time, substitute a different XX into the algebraic representation and identify its YY. Mark all the points obtained on the drawing and then draw a straight line between them.

For example:
Y=3X2Y=3X-2
Let's substitute three XXs and we get:

XXYY
0-2
111-1
244


Now let's mark the points we obtained on the number line:

*Illustration in Word file*

Examples of graphical representation of a function:

*Illustrations in Word file – (It is advisable to draw a number line with numbers)*

Important tips:
How do you know if the function is increasing or decreasing?
There are 2 ways:

  1. According to the coefficient of XX in the algebraic representation – if the coefficient of XX is positive, the function increases from left to right. If negative, the function decreases from left to right.
  2. Mark 33 points of the function (substitute a different XX each time and find the YY) and then draw a straight line passing through them. Look from left to right and decide if the function is increasing or decreasing.

You can read more about the graphical representation of a function at this link!

Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Test your knowledge

Tabular representation of a function

A tabular representation is essentially a representation using a table of XX and YY showing us the value of YY for each XX that we substitute into the function.

Let's see an example:
For the algebraic representation - Y=4X1Y=4X-1
we get a tabular representation like this:

YYXX
1-10​ 0​
3311
7722
111133
151544

Verbal representation of a function

A verbal representation of a function describes the relationship between XX and YY using words.

For example:
Each package of flour (XX) makes 33 whole pizzas (YY)

Y=3XY=3X

For more information on verbal and tabular representation of a function, click here!

Do you know what the answer is?

Function notation

How do we denote a function?
So far, we have denoted a function as Y=Y=……
It is also useful to know that a function can be denoted in the following way:
F(x)=...F(x)=……... which implies that we will get a value that depends on XX.

You can read more about function notation here!

Check your understanding
Start practice