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# P2 Functions - Range and Domain? watch

1. The functions f and g are defined by:

f: x |--> x2 - 2x + 3 XER 0 ≤ x ≤ 4

(a) Find the range of f. (3marks)

I simply dont know how to find out the range in a functions question. What do you have to do? Is it the same process in each type of question?
Could someone quickly explain the range...

Also, whats the domain?
2. (Original post by cherc2005)
The functions f and g are defined by:

f: x |--> x2 - 2x + 3 XER 0 ≤ x ≤ 4

(a) Find the range of f. (3marks)

I simply dont know how to find out the range in a functions question. What do you have to do? Is it the same process in each type of question?
Could someone quickly explain the range...

Also, whats the domain?
The range is f>=-1. The range is the set of values which f(x) can take i.e. the y values. The easiest thing to do is to differentiate to find either a min or max point, or put it in your graphical calculator.

So if you get a question just think the set of values of y, and obviously in this case, the minimum point is y=-1 so no y value can be less than -1, so it must be greater than or equal to -1, hope this helps.
3. (Original post by eltombarno52)
The range is f>=-1. The range is the set of values which f(x) can take i.e. the y values. The easiest thing to do is to differentiate to find either a min or max point, or put it in your graphical calculator.

So if you get a question just think the set of values of y, and obviously in this case, the minimum point is y=-1 so no y value can be less than -1, so it must be greater than or equal to -1, hope this helps.
You can't always do this though and really range/domain questions can be fairly tough.

There is no special technique, you just need a good knowledge of a wide range of functions.

If you get a simple polynomial (as above) then differentiate. But this isn't always perfect. Imagine a cubic function. You differentiate and get a quadratic which you solve finding two x values at which there are stationary points. You can then go on to find which are max / min with the 2nd derrivative.

However it is all in vain. A cubic can produce all y values (given the domain is not "artificially" restricted) remember the up/down/up graph.

So my technique is just think of the graph.
4. Domain is given 0 ≤ x ≤ 4

Find minimum by differenciation:

y = x^2 - 2x + 3
dy/dx = 2x - 2

minimum occurs when dy/dx = 0

2x = 2
x = 1

therefore minimum is...

f(1) = 1 - 2 + 3

therefore minimum value of f(x) is 2!!!

maximum value occurs when x = 4

f(4) = 4^2 - 2(4) + 3
f(4) = 11

therefore the range of values for the function between 2 and 11

can someone say if this is correct plz

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