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If f ( x ) = x 2 - 4 , calculate b if f ( b ) = 45 .

  1. f ( b ) = b 2 - 4 but f ( b ) = 45
  2. b 2 - 4 = 45 b 2 - 49 = 0 b = + 7 or - 7


  1. Guess the function in the form y = ... that has the values listed in the table.
    x 1 2 3 40 50 600 700 800 900 1000
    y 1 2 3 40 50 600 700 800 900 1000
  2. Guess the function in the form y = ... that has the values listed in the table.
    x 1 2 3 40 50 600 700 800 900 1000
    y 2 4 6 80 100 1200 1400 1600 1800 2000
  3. Guess the function in the form y = ... that has the values listed in the table.
    x 1 2 3 40 50 600 700 800 900 1000
    y 10 20 30 400 500 6000 7000 8000 9000 10000
  4. On a Cartesian plane, plot the following points: (1;2), (2;4), (3;6), (4;8), (5;10). Join the points. Do you get a straight line?
  5. If f ( x ) = x + x 2 , write out:
    1. f ( t )
    2. f ( a )
    3. f ( 1 )
    4. f ( 3 )
  6. If g ( x ) = x and f ( x ) = 2 x , write out:
    1. f ( t ) + g ( t )
    2. f ( a ) - g ( a )
    3. f ( 1 ) + g ( 2 )
    4. f ( 3 ) + g ( s )
  7. A car drives by you on a straight highway. The car is travelling 10 m every second. Complete the table below by filling in how far the car has travelledaway from you after 5, 10 and 20 seconds.
    Time (s) 0 1 2 5 10 20
    Distance (m) 0 10 20
    Use the values in the table and draw a graph of distance on the y -axis and time on the x -axis.

Characteristics of functions - all grades

There are many characteristics of graphs that help describe the graph of any function. These properties will be described in this chapter and are:

  1. dependent and independent variables
  2. domain and range
  3. intercepts with axes
  4. turning points
  5. asymptotes
  6. lines of symmetry
  7. intervals on which the function increases/decreases
  8. continuous nature of the function

Some of these words may be unfamiliar to you, but each will be clearly described. Examples of these properties are shown in [link] .

(a) Example graphs showing the characteristics of a function. (b) Example graph showing asymptotes of a function. The asymptotes are shown as dashed lines.

Dependent and independent variables

Thus far, all the graphs you have drawn have needed two values, an x -value and a y -value. The y -value is usually determined from some relation based on a given or chosen x -value. These values are given special names in mathematics. The given or chosen x -value is known as the independent variable, because its value can be chosen freely. The calculated y -value is known as the dependent variable, because its value depends on the chosen x -value.

Domain and range

The domain of a relation is the set of all the x values for which there exists at least one y value according to that relation. The range is the set of all the y values, which can be obtained using at least one x value.

If the relation is of height to people, then the domain is all living people, while the range would be about 0,1 to 3 metres — no living person can have a height of 0m, and while strictly it's not impossible to be taller than 3 metres, no one alive is. An important aspect of this range is that it does not contain all the numbers between 0,1 and 3, but at most six billion of them (as many as there are people).

As another example, suppose x and y are real valued variables, and we have the relation y = 2 x . Then for any value of x , there is a value of y , so the domain of this relation is the whole set of real numbers. However, we know that no matter what value of x we choose, 2 x can never be less than or equal to 0. Hence the range of this function is all the real numbers strictly greater than zero.

Questions & Answers

how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
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Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
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for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
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what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [ncs]. OpenStax CNX. Aug 05, 2011 Download for free at http://cnx.org/content/col11239/1.2
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