Representing a Function Verbally and with Tables

🏆Practice function representation

Function, describes a correlation or coincidence between a dependent variable (Y Y ) and an independent variable (X X ). The legitimacy of this relationship between the variables is called the " correspondence rule ".

Verbal representation of a function

The verbal representation of a function expresses the connection between variables verbally, i.e. through a story.

A typical verbal representation of a function can look like this:

  • Assuming that Daniel reads all the books he buys that month, the total number of books Daniel reads per year (Y Y ) is a function of the number of books Danny buys each month (X X ).

Tabular representation of a function

A tabular representation of a function is a demonstration of the legitimacy of a function using a table of values X X (independent variable) and the corresponding values Y Y (dependent variable).

In general, a table of values is shown as follows:

A1 - Verbal representation of a new function

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Test yourself on function representation!

einstein

Is the given graph a function?

–4–4–4–3–3–3–2–2–2–1–1–1111222333444–2–2–2–1–1–1111222000

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Examples of exercises on verbal and tabular representation of a function

Example 1

Y Y is a function of X X that corresponds to any value of X X a number less than it in 2 2 .

Y=X2 Y=X-2

Solve the equation for each of the numbers of X X represented in the following table and place the correct number in. Y Y .

verbal and tabular representation of a function

If X=1 X = 1 , then Y will be equal to ____________

If X=13 X = 13 , then Y will equal ___________ .

A value of X X corresponding to Y=10,5 Y = 10,5 is __________

A value X X corresponding to Y=0 Y = 0 is __________


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Practice of verbal and tabular representation of a function

Example 2

Describe in words the relationship between X X e Y Y .

Describe in words the relationship between X and Y.


Example 3

Write down which table represents a function and which table does not represent a function

which does not represent a function


Do you know what the answer is?

Example 4

Y Y is a function of X X that corresponds to any value of X X a number that is 5 5 times greater than it.

Y=5X Y=5X

Complete the table of values

a function of X corresponding to any value of X
  • If X=1 X = 1 , then Y Y will equal ____________
  • If X=13 X = 13 , then Y Y will be equal to ____________
  • If Y=10,5 Y = 10,5 , then X X will be equal to ____________
  • If Y=0 Y = 0 , then X X will be equal to ____________

Example 5

Y Y is a function of X X that corresponds to any value of X X a number 4 4 times less than it.

Y=X4 Y=\frac{X}{4}

Complete the table of values

a function of X corresponding to any value of X
  • If X=1 X = 1 , then Y Y will be equal to ____________
  • If X=13 X = 13 , then Y Y will be equal to ____________
  • If Y=10,5 Y = 10,5 , then X X will be equal to ____________
  • If Y=0 Y = 0 , then X X will be equal to ____________

Check your understanding

Example 6

Complete the following table

Complete the following table
  • If X=10 X = 10 , then Y Y will equal ____________
  • If X=2 X = -2 , then Y Y will be equal to ____________
  • If Y=100 Y = 100 , then X X will be equal to ____________
  • If Y=20 Y = -20 , then X X will be equal to ____________

Example 7

Answer the following questions (for each example, write a table of values and draw the graph)

  • Write an example of a function whose graph describes it as a continuous graph.
  • Write an example of a function whose graph is discrete.

Do you think you will be able to solve it?

Example 8

The function Y Y corresponds to any number X X that is its root.

Y=X Y=\sqrt{X}

Complete the table of values

a function of X corresponding to any value of X
  • If X=1 X = 1 , then Y Y will be equal to ____________
  • If X=13 X = 13 , then Y Y will be equal to ____________
  • If Y=10,5 Y = 10,5 , then X X will be equal to ____________
  • If Y=0 Y = 0 , then X X will be equal to ____________

Example 9

The function corresponds to any number X X less than 3 3 of half the number

Y=X23 Y=\frac{X}{2}-3

  • Complete the table of values
a function of X corresponding to any value of X
  • If X=1 X = 1 , then Y Y will be equal to ____________
  • If X=13 X = 13 , then Y Y will be equal to ____________
  • If Y=10,5 Y = 10,5 , then X X will be equal to ____________
  • If Y=0 Y = 0 , then X X will be equal to ____________

Test your knowledge

Example 10

The function Y Y corresponds to any number X X greater in 5 5 times the number

Y=2X+5 Y=2X+5

  • Complete the table of values
a function of X corresponding to any value of X

  • If X=1 X = 1 , then Y Y will be equal to ____________
  • If X=13 X = 13 , then Y Y will be equal to ____________
  • If Y=10,5 Y = 10,5 , then X X will be equal to ____________
  • If Y=0 Y = 0 , then X X will be equal to ____________

Review questions

What is a function?

A function is a relationship between two variables, the variable Y Y which is called the dependent variable, and the variable X X , which is called the independent variable, between these two variables there is a correspondence rule; that is, for each value of X X there is only one value of Y Y .


What are the ways of representing a relationship?

A function can be represented as follows:

  • Verbally
  • Algebraically
  • Table of values (Tabular)
  • Graphically.

How to represent functions step by step?

Let's see an example of how to represent a function.

Example:

Represent the following function in its different forms

  • Verbally:

Let Y Y be a function of X X such that a value of X X corresponds to a number increased by 4 4

  • Algebraically:

Y=X+4 Y=X+4

  • Table of values:

We already have the function in algebraic form, now we are going to give values to X X , to find the value of Y Y , according to the correspondence rule, and these values we are going to register them in a table:

1 - How to represent functions step by step

Now we are going to substitute the values of X X , to register the value that corresponds to Y Y , let's start with

We already know that the algebraic expression of this function is:

Y=X+4 Y=X+4

Then,

When X=4 X=-4

Y=4+4=0 Y=-4+4=0

When X=3 X=-3

Y=3+4=1 Y=-3+4=1

When X=1 X=-1

Y=1+4=3 Y=-1+4=3

When X=0 X=0

Y=0+4=4 Y=0+4=4

When X=2 X=2

Y=2+4=6 Y=2+4=6

When X=5 X=5

Y=5+4=9 Y=5+4=9

According to this data we are now going to record it in the table

2 - How to represent functions step by step

We have represented the function in a table of values.

  • Graphically:

Finally we are going to represent these values in a graph:

We are going to find the pairs of coordinates in the Cartesian plane, and join each point as follows.

3 - How to represent functions step by step

We can see that the function in graphical form is a linear function because it forms a straight line.


Do you know what the answer is?
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