# Numerical Value

🏆Practice equation (+ what is the unknown)

## Value

### What is value?

Value in mathematics indicates how much something is worth numerically.

### What is the value of the function?

The word value signifies how much the function "is worth" – that is, what the value of $Y$ will be in the function when we substitute any number in $X$.

### What is a table of values?

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

### What is absolute value?

The distance of the number in absolute value from the digit $0$.
It will always be positive because it is a distance.

## Test yourself on equation (+ what is the unknown)!

Find a y when $$x=2$$

$$y=5x$$

## Value

### What is value in real life?

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.

### What is value in mathematics?

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 $100$.

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

### What is the value of the function?

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 $8$.

### What is a table of values?

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:

 Sure, please provide the text you would like translated. Sure, please provide the text you would like to be translated. 0 2 1 3 2 6
Do you know what the answer is?

### What is absolute value?

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
$|-4|=4$

## Examples with solutions for Equation (+ what is the unknown)

### Exercise #1

$\left|18\right|=$

### Step-by-Step Solution

The "absolute value" can be viewed as the distance of a number from 0.
Therefore, the absolute value will not change the sign from negative to positive, it will always be positive.

$18$

### Exercise #2

Calculate y given that $x=2$ and $y=x$.

### Step-by-Step Solution

We are given the equation y=x

We are also given the value of x,

x=2

Therefore, we will substitute the given value into the equation

y=2

And that's the solution!

$2$

### Exercise #3

Find a y when x=2

$y=\frac{2}{5}x+2$

### Step-by-Step Solution

In this exercise, we are given the value of X, so we will substitute it into the formula.

It's important to remember that between an unknown and a number there is a multiplication sign, therefore:

y=2/5*(2)+2

y=4/5+2

Let's convert to a decimal fraction:

y=0.8+2
y=2.8

And that's the solution!

$2.8$

### Exercise #4

Find a y when $x=2$

$y=5x$

10

### Exercise #5

$\left|3\right|=$

### Video Solution

$3$