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Range of a Function OCR ALevel

Hi,

Please can someone provide a method or example to find the range of a function.

Please I really dont understand this or the domain :smile:

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The domain of a function is the set of values which can be passed to a function as an argument.

Some people use the word range to mean codomain, some people use the word range to mean image.
The image of a function is the set of values which the function may return as an answer. The codomain of a function is a set of values that has the image as a subset.
Original post by Phideaux
The domain of a function is the set of values which can be passed to a function as an argument.

Some people use the word range to mean codomain, some people use the word range to mean image.
The image of a function is the set of values which the function may return as an answer. The codomain of a function is a set of values that has the image as a subset.

I understand this and range corresponds to y values whereas domain corresponds to x values but not sure how to find them?
By range do you mean image or codomain?
Do you understand the difference?
It is ok to say you don't know!
(edited 3 years ago)
Original post by Phideaux
By range do you mean image or codomain?
Do you understand the difference?

Not properly, I'm just trying to find the range as you would at A-Level (OCR)?
I suspect you probably mean image.
Consider the function...

f(n): N -> N = n^2

Do you understand this notation?
It is ok to say no.
Original post by Phideaux
I suspect you probably mean image.
Consider the function...

f(n): N -> N = n^2

Do you understand this notation?
It is ok to say no.

No, sorry please can you explain?

I feel dumb but just to put into perspective this is my second year prep work :smile:
The first N means the function f takes arguments from the set N, that is the set of natural numbers ie: the positive whole numbers {1, 2, 3, 4,...}. This is the domain.

The second N means the function f returns answers that are taken from N, the same set of natural numbers. This is the codomain. We could equally define our codomain to be Z, that is the set of integers ie: the set of whole numbers, either positive, negative or zero. Remember not every number in the codomain has to be the answer f returns for some number in the domain.

The image of this particular function f is the set of values in the codomain that f returns as answers when f is passed some (valid) argument from the domain.
So the image (which is I think what you are asking about) is {1, 4, 9, 16,...}
(edited 3 years ago)
Observe that the image {1, 4, 9, 16,...} is a subset of the codomain N
N being shorthand for {1, 2, 3 4,,...}
Thank you.

So is I was to find the range of:

f (x) = 63 / (4x-1) for the values 1<= x <= 16

Would this be correct:
1<= y >= 21?
You have the right numbers but the second inequality is pointing the wrong way

it should be 1 =< y =< 21
Original post by M.Johnson2111
No, sorry please can you explain?

I feel dumb but just to put into perspective this is my second year prep work :smile:

For the A level, I think this is all you need to know : https://youtu.be/Kc-fVGvPRQg

You are expected to draw the graphs out if you need to find the range, like they will give you a quadratic , cubic or caustic graph if they want you to find the range. Or they will tell you the x value corresponding to the limits of the range and expect you to find the range by substituting in this value.

I do Edexcel though, however , the stuff to do with codomains and images sounds like FM or uni level tbh.
Original post by Phideaux
You have the right numbers but the second inequality is pointing the wrong way

it should be 1 =< y =< 21

Thank you very much
Original post by lhh2003
For the A level, I think this is all you need to know : https://youtu.be/Kc-fVGvPRQg

You are expected to draw the graphs out if you need to find the range, like they will give you a quadratic , cubic or caustic graph if they want you to find the range. Or they will tell you the x value corresponding to the limits of the range and expect you to find the range by substituting in this value.

I do Edexcel though, however , the stuff to do with codomains and images sounds like FM or uni level tbh.

Thank you, that's what I thought :smile:
you are allowed to use a graphical calculator in the exams: this helps to check if your answers for range ( y values ) and domain ( x values ) are correct.
Original post by lhh2003
For the A level, I think this is all you need to know : https://youtu.be/Kc-fVGvPRQg

You are expected to draw the graphs out if you need to find the range, like they will give you a quadratic , cubic or caustic graph if they want you to find the range. Or they will tell you the x value corresponding to the limits of the range and expect you to find the range by substituting in this value.

I do Edexcel though, however , the stuff to do with codomains and images sounds like FM or uni level tbh.

If I were to have:
f (x) = 4x^2 - 12x

To find the range would I solve the equation and sub the lower and upper value?
Original post by the bear
you are allowed to use a graphical calculator in the exams: this helps to check if your answers for range ( y values ) and domain ( x values ) are correct.

I've heard this, but how do you do it please I have one with me now?
Original post by M.Johnson2111
If I were to have:
f (x) = 4x^2 - 12x

To find the range would I solve the equation and sub the lower and upper value?

That would often work but not necessarily. Consider what the image would be if you restrict the domain to the set of values from 1 to 4.

Clue: what is f(3/2) ?

Unless you have done finding minimum and maximum points using calculus the easiest way would be to draw a graph.
(edited 3 years ago)
Original post by Phideaux
That would often work but not necessarily. Consider what the image would be if you restrict the domain to the set of values from 1 to 4.

Clue: what is f(3/2) ?

Unless you have done finding minimum and maximum points using calculus the easiest way would be to draw a graph.

Okay so the roots are (0,0) and (3,0)
The minimum point is (3/2,-8)
So is the range just y >= -8?
The image here is going to be the set of values from the minimum value f returns for values of x from 1 to 4 ...which is -9 (achieved when x = 3/2)
to the maximum value f returns for values of x from 1 to 4 ...which is 16 (achieved when x = 4).

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