# C3 functions

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I know for some functions drawing the graph helps but what about complicated functions for which drawing a graph would be a pain in exams?

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#3

(Original post by

I know for some functions drawing the graph helps but what about complicated functions for which drawing a graph would be a pain in exams?

**Brudor2000**)I know for some functions drawing the graph helps but what about complicated functions for which drawing a graph would be a pain in exams?

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(Original post by

Give an example of a 'complicated' function.

**RDKGames**)Give an example of a 'complicated' function.

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#5

The main thing to do is see if there are any values where f(x) doesn't exist. For example, if you have something like

1/(x-2)

we know that the denominator of a fraction can't be equal to zero. This means that x-2 must not be equal to 0.

If we actually think about what happens at x=2, we understand that the function approaches infinity, and therefore has an asymptote there.

Look at the attached file to see the asymptote.

1/(x-2)

we know that the denominator of a fraction can't be equal to zero. This means that x-2 must not be equal to 0.

If we actually think about what happens at x=2, we understand that the function approaches infinity, and therefore has an asymptote there.

Look at the attached file to see the asymptote.

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(Original post by

The main thing to do is see if there are any values where f(x) doesn't exist. For example, if you have something like

1/(x-2)

we know that the denominator of a fraction can't be equal to zero. This means that x-2 must not be equal to 0.

If we actually think about what happens at x=2, we understand that the function approaches infinity, and therefore has an asymptote there.

Look at the attached file to see the asymptote.

**Kota Dagnino**)The main thing to do is see if there are any values where f(x) doesn't exist. For example, if you have something like

1/(x-2)

we know that the denominator of a fraction can't be equal to zero. This means that x-2 must not be equal to 0.

If we actually think about what happens at x=2, we understand that the function approaches infinity, and therefore has an asymptote there.

Look at the attached file to see the asymptote.

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#7

(Original post by

well i cant't think of or find one rn. even if function is not complicated is there another way to find the domain other than drawing a graph.

**Brudor2000**)well i cant't think of or find one rn. even if function is not complicated is there another way to find the domain other than drawing a graph.

But Generally drawing a graph will help

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(Original post by

so the domain is (-infinity,2) and (2, infinity)

**Kota Dagnino**)so the domain is (-infinity,2) and (2, infinity)

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(Original post by

well you don't always have to draw a graph if you know the general shape of the function. For example if you have something like f(x)= x-5/x+1, then the domain would be all real values of x apart from x=-1 (as then you would get -6/0 which is undefined).

But Generally drawing a graph will help

**Anonymouspsych**)well you don't always have to draw a graph if you know the general shape of the function. For example if you have something like f(x)= x-5/x+1, then the domain would be all real values of x apart from x=-1 (as then you would get -6/0 which is undefined).

But Generally drawing a graph will help

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#12

**Brudor2000**)

well i cant't think of or find one rn. even if function is not complicated is there another way to find the domain other than drawing a graph.

Otherwise, you can get rational functions like which are undefined at only and so this function is valid for all reals except those two numbers.

The product of the two functions mentioned, would constitute to a domain that is except and .

So really, you should know by heart the domain of your basic special functions in C3 like , and that the denominators cannot ever be equal to 0, then apply these to more complicated functions which combine the two.

Forgot what's in C3 so I just used these two examples to illustrate the typical procedure.

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what about range of an equation when they have given a domain such as x is all real number???

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#14

Basically, if you have a domain that looks like this (x,X) then its range will be (f(x), f(X)).

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#15

(Original post by

Basically, if you have a domain that looks like this (x,X) then its range will be (f(x), f(X)).

**Kota Dagnino**)Basically, if you have a domain that looks like this (x,X) then its range will be (f(x), f(X)).

Example: for

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**Kota Dagnino**)

Basically, if you have a domain that looks like this (x,X) then its range will be (f(x), f(X)).

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#18

if they say that the domain is all real numbers, then the range will also be all real numbers

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(Original post by

if they say that the domain is all real numbers, then the range will also be all real numbers

**Kota Dagnino**)if they say that the domain is all real numbers, then the range will also be all real numbers

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