Numerical Value

When we ask if something has value, we are essentially asking if it has meaning and if it is "worth" something.
For example, we might ask, how much value does this ring have? And we would expect an answer that describes how much this ring is worth.
We might get an answer like – the sentimental value of the ring is high for me because my grandmother gave it to me as a gift, but its real value – its worth in monetary or numerical terms – is low.

Value in mathematics indicates how much something is worth numerically.
If we take the ring as an example, we can ask what the value of the ring is, and the answer in mathematics would be, for example – $100$ dollars.
If we represent $X$ as the price of the ring, or the value of the ring, we get: $X=100$. We can say that the value of $X$ is $100$.
Or in other words, $X$ equals $100$.

As we have just learned, the word value signifies how much the function "equals" – that is, what the $Y$ of the function is when we substitute any number.

Let's see an example and understand better:
Given the function $Y=5X+3$
What is the value of the function when $X=5$?
Solution –
We are essentially asked what $Y$ will be when $X$ is $5$.
We substitute $X=5$ and get:
$y=5*5+3$
$​​​​​​​Y=28$
When $X=5$ the value of the function is $28$.

Another example:
Given the function $Y=2X+4$
when the value of $X$ is $2$, what is the value of the function?

Solution:
Note that we are given that the value of $X$ is 2, which means $X=2$.
We are asked for the value of the function – that is, what $Y$ will be equal to if $X=2$
Therefore, we substitute $X=2$ into the function and get the value of $Y$:
$Y=2*2+4$
$Y=8$
We found that when $X=2$, the value of the function is $8$.

The values in the value table indicate how much $Y$ of that function will be worth when we substitute $X$ with different values.

For example:
Given the function $Y=X^2+2$
create a table of values for $3$,$X$.

Solution:
We were asked to build a value table for the given function with $3$ different $X$ values.
We choose $X=0$, $X=2$, $X=1$
We will substitute each different value into the function and get the value of $Y$.
We get:

The meaning of absolute value is slightly different from the meaning of a regular value.
When asked what the absolute value of a number is, we are essentially asking what its distance is from the number $0$.
Therefore, it doesn't matter if the number is positive or negative, the distance – the absolute value, will always be positive.
It is customary to denote absolute value with two parallel lines.

Let's see an example:
$|4|=$

Solution:
When the number is between two parallel lines as in the example, it is in absolute value.
What is the distance of $4$ from the number $0$? 
$4$!
Therefore:
$|4|=4$

Another exercise:
$|-4|=$

Solution:
We ask what is the distance of $4-$ from the number $0$?
$4$!
Therefore also
$|-4|=4$