[fayled]

How do you find the range of a function?

I know it involves the use of a graph sketch but the book doesn't make it clear how to interpret it.

Thanks.

[TenOfThem]

Depends on the function

If it has a restricted domain then the extremes of that may impact
If it has turning point(s) they will impact

[fayled]

Say g(x)=2x^2+3

How would you find the range?

[notnek]

(Original post by fayled)
Say g(x)=2x^2+3

How would you find the range?

A square number is always ____ so the output of g must be real numbers _____ .

[nuodai]

(Original post by fayled)
Say g(x)=2x^2+3

How would you find the range?

There are a few ways. One way is to notice that and derive a similar inequality for .

Another method in this case is to sketch it (or at least think of the sketch). When you sketch the graph of a function to find its range, what's important is the y-axis. Now, the graph of only contains points above (or on) the x-axis, and by a sequence of two graph transformations you can work out how this changes when we consider .

Generally if has a range that you know, and is the function obtained by graph transformations of the form , then you can work out the range of by considering the transformations that affect the y-axis (i.e. the 'a' and 'b' above). In particular, if is in the range of then is in the range of . So for instance if has range then has range .

[Mehjabeen]

The range is the set of values of y for which the function is valid. If you draw the graph of this curve, you will find that when X= 0, Y=3. Now this 3 is the smallest value of y in the curve if you notice. So the range should be Y> or = 3 when X is applicable for all real values. The curve extends upwards and so every Y coordinates of it is more than 3.

[fayled]

Right I got it, so obviously some functions have an unlimited range such as cubics?

[TenOfThem]

(Original post by fayled)
Right I got it, so obviously some functions have an unlimited range such as cubics?

only if their domain is R

with a restricted domain they would have a restricted range