1.7 Function notation

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This module describes notation for functions.

Function notation

Functions are represented in math by parentheses. When you write $f\left(x\right)$ you indicate that the variable $f$ is a function of—or depends on—the variable $x$ .

For instance, suppose $f\left(x\right)={x}^{2}+3x$ . This means that f is a function that takes whatever you give it, and squares it, and multiplies it by 3, and adds those two quantities.

 $\begin{array}{c}7\to \\ \text{10}\to \\ x\to \\ y\to \\ \text{a dog}\to \end{array}$ $\begin{array}{c}\to f\left(7\right)={7}^{2}+3\left(7\right)=\text{70}\\ \to f\left(\text{10}\right)={\text{10}}^{2}+3\left(\text{10}\right)=\text{130}\\ \to f\left(x\right)={x}^{2}+3x\\ \to f\left(y\right)={y}^{2}+3y\\ \begin{array}{}\to f\left(\text{dog}\right)={\left(\text{dog}\right)}^{2}+3\left(\text{dog}\right)\\ \left(\text{*not in the domain}\right)\end{array}\end{array}$

The notation $f\left(7\right)$ means “plug the number 7 into the function $f$ .” It does not indicate that you are multiplying $f$ times 7. To evaluate $f\left(7\right)$ you take the function $f\left(x\right)$ and replace all occurrences of the variable x with the number 7. If this function is given a 7 it will come out with a 70.

If we write $f\left(y\right)={y}^{2}+3y$ we have not specified a different function . Remember, the function is not the variables or the numbers, it is the process. $f\left(y\right)={y}^{2}+3y$ also means “whatever number comes in, square it, multiply it by 3, and add those two quantities.” So it is a different way of writing the same function.

Just as many students expect all variables to be named $x$ , many students—and an unfortunate number of parents—expect all functions to be named $f$ . The correct rule is that—whenever possible— functions, like variables, should be named descriptively . For instance, if Alice makes \$100/day, we might write:

• Let m equal the amount of money Alice has made (measured in dollars)
• Let t equal the amount of time Alice has worked (measured in days)
• Then, $m\left(t\right)=\text{100}t$

This last equation should be read “ $m$ is a function of $t$ (or $m$ depends on $t$ ). Given any value of the variable $t$ , you can multiply it by 100 to find the corresponding value of the variable $m$ .”

Of course, this is a very simple function! While simple examples are helpful to illustrate the concept, it is important to realize that very complicated functions are also used to model real world relationships. For instance, in Einstein’s Special Theory of Relativity, if an object is going very fast, its mass is multiplied by $\frac{1}{\sqrt{1-\frac{{v}^{2}}{9\cdot {\text{10}}^{\text{16}}}}}$ . While this can look extremely intimidating, it is just another function. The speed $v$ is the independent variable, and the mass $m$ is dependent. Given any speed $v$ you can determine how much the mass $m$ is multiplied by.

Questions & Answers

who was the first nanotechnologist
Lizzy Reply
k
Veysel
technologist's thinker father is Richard Feynman but the literature first user scientist Nario Tagunichi.
Veysel
Norio Taniguchi
puvananathan
Interesting
Andr
I need help
Richard
anyone have book of Abdel Salam Hamdy Makhlouf book in pdf Fundamentals of Nanoparticles: Classifications, Synthesis
Naeem Reply
what happen with The nano material on The deep space.?
pedro Reply
It could change the whole space science.
puvananathan
the characteristics of nano materials can be studied by solving which equation?
sibaram Reply
plz answer fast
sibaram
synthesis of nano materials by chemical reaction taking place in aqueous solvents under high temperature and pressure is call?
sibaram
hydrothermal synthesis
ISHFAQ
how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
STM - Scanning Tunneling Microscope.
puvananathan
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Source:  OpenStax, Advanced algebra ii: conceptual explanations. OpenStax CNX. May 04, 2010 Download for free at http://cnx.org/content/col10624/1.15
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