Representing a Function Verbally and with Tables

Examples of exercises on verbal and tabular representation of a function

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

$Y=X-2$

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

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

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

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

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

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

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

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

$Y=5X$

Complete the table of values

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

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

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

Complete the table of values

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

Complete the following table

• If $X = 10$, then $Y$ will equal ____________
• If $X = -2$, then $Y$ will be equal to ____________
• If $Y = 100$, then $X$ will be equal to ____________
• If $Y = -20$, then $X$ will be equal to ____________

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.

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

$Y=\sqrt{X}$

Complete the table of values

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

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

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

• Complete the table of values

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

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

$Y=2X+5$

• Complete the table of values

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

What is a function?

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

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

• Algebraically:

$Y=X+4$

• Table of values:

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

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

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

$Y=X+4$

Then,

When $X=-4$

$Y=-4+4=0$

When $X=-3$

$Y=-3+4=1$

When $X=-1$

$Y=-1+4=3$

When $X=0$

$Y=0+4=4$

When $X=2$

$Y=2+4=6$

When $X=5$

$Y=5+4=9$

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

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.

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

If you are interested in this article you may also be interested in the following articles:

Graphical representation of a function

Algebraic representation of a function

Notation of a function

Domain of a function

Indefinite integral

Numerical value assignment in a function

Increasing function

Decreasing function

Constant function

Growing and decreasing intervals of a function

Functions for seventh grade

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