# 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.

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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
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
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I only see partial conversation and what's the question here!
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yes that's correct
Professor
I think
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if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
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analytical skills graphene is prepared to kill any type viruses .
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Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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write examples of Nano molecule?
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The nanotechnology is as new science, to scale nanometric
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nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
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?
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yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
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biomolecules are e building blocks of every organics and inorganic materials.
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how did you get the value of 2000N.What calculations are needed to arrive at it
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