What is the difference in writing the range of values of a function

In summary, the range of a function is the set of all possible output values, while the domain is the set of all possible input values. Writing the range of values is important because it gives a complete understanding of the function and allows us to see the full scope of the relationship between the input and output values. A finite range means there is a limited set of possible output values, while an infinite range means there is an unlimited set of possible output values. The range of a function can be determined by graphing the function or analyzing its equation for restrictions or patterns.
  • #1
mathlearn
331
0
I was just wondering in writing the range of values for which the function is increasing or decreasing in in a positive or a negative way ,

The difference caused by the use of the symbols $'>'$ and $'≥'$ or in $'<'$ or $'≤ '$​

For example If we consider the graph of the function,

$y=\left(x-x\right)^2-5$ & asked to write down the interval of values of $x$ on which the function increases from $-5$ to $3$

The range can be written as & note here that $'≤'$ is used instead of $<$

$2≤ x≤ 4.8$

& taking another graph in the form of $y=2-x(x-4)-2$

write down the interval of $x$ in which the function is positive and increasing

$-1<x<1$

So what is the difference in the use of symbol $<$ & $≤$ in writing the range
 
Mathematics news on Phys.org
  • #2
Re: What is the difference in writing the range of values of a funtion

mathlearn said:
I was just wondering in writing the range of values for which the function is increasing or decreasing in in a positive or a negative way ,

The difference caused by the use of the symbols $'>'$ and $'≥'$ or in $'<'$ or $'≤ '$​

For example If we consider the graph of the function,

$y=\left(x-x\right)^2-5$ & asked to write down the interval of values of $x$ on which the function increases from $-5$ to $3$

The range can be written as & note here that $'≤'$ is used instead of $<$

$2≤ x≤ 4.8$

& taking another graph in the form of $y=2-x(x-4)-2$

write down the interval of $x$ in which the function is positive and increasing

$-1<x<1$

So what is the difference in the use of symbol $<$ & $≤$ in writing the range

Hey mathlearn! ;)

Both forms are fine and usually mean the same thing.
The difference is whether we want to include the end points or not.
And that difference is only relevant if the function is not defined or makes a jump at an end point.
If it's already known that the function is well defined and continuous, as in your examples, that can't happen.
 
  • #3
Re: What is the difference in writing the range of values of a funtion

Thank you very much ILS :)

I like Serena said:
Hey mathlearn! ;)

Both forms are fine and usually mean the same thing.
The difference is whether we want to include the end points or not.
And that difference is only relevant if the function is not defined or makes a jump at an end point.
If it's already known that the function is well defined and continuous, as in your examples, that can't happen.

Hey I like Serena :D,

So then when we are asked to write an exact range like in,

mathlearn said:
$y=\left(x-x\right)^2-5$ & asked to write down the interval of values of $x$ on which the function increases from $-5$ to $3$

The range can be written as & note here that $'≤'$ is used instead of $<$

$2≤ x≤ 4.8$

we must be using the $≤ $ symbol

or if we are asked to write the range of values of which the function is increasing or decreasing negatively or positively in which we aren't given a limit using numbers we use $<$, Like in

mathlearn said:
write down the interval of $x$ in which the function is positive and increasing

$-1<x<1$

So what is the difference in the use of symbol $<$ & $≤$ in writing the range

Many Thanks (Smile)
 
  • #4
Re: What is the difference in writing the range of values of a funtion

mathlearn said:
So then when we are asked to write an exact range like in,

mathlearn said:
$y=\left(x-x\right)^2-5$ & asked to write down the interval of values of $x$ on which the function increases from $-5$ to $3$

The range can be written as & note here that $'≤'$ is used instead of $<$

$2≤ x≤ 4.8$

we must be using the $≤ $ symbol

The text "from $-5$ to $3$" is ambiguous to whether the end points are included, so we are free to pick either. ;)

or if we are asked to write the range of values of which the function is increasing or decreasing negatively or positively in which we aren't given a limit using numbers we use $<$, Like in

mathlearn said:
write down the interval of $x$ in which the function is positive and increasing

$-1<x<1$

So what is the difference in the use of symbol $<$ & $≤$ in writing the range

Many Thanks (Smile)

In this case we should certainly not include -1 or 1 in the range, since they are specifically excluded. (Nerd)
 

FAQ: What is the difference in writing the range of values of a function

What is the range of a function?

The range of a function is the set of all possible output values, or the set of all values that the function can produce.

How is the range of a function different from the domain?

The domain of a function is the set of all possible input values, while the range is the set of all possible output values. In other words, the domain is the set of independent variables, while the range is the set of dependent variables.

Why is it important to write the range of values when describing a function?

Writing the range of values is important because it helps to give a complete understanding of the function. It allows us to see the full scope of the function and understand how the input values are related to the output values.

What is the difference between a finite and infinite range?

A finite range means that there is a limited set of possible output values for the function, while an infinite range means that there is an unlimited set of possible output values. This can also be interpreted as a bounded or unbounded range.

How can the range of a function be determined?

The range of a function can be determined by graphing the function and identifying the highest and lowest points on the graph. It can also be determined by analyzing the function's equation and identifying any restrictions or patterns in the output values.

Similar threads

Back
Top