domains and ranges of graphs HELPPP (a-level maths)

i have watched so many youtube videos and my teachers explained it 34734398794 million times but i still cannot find the domain and ranges of functions and like graphs

could anyone idek have a way to acc understand and explain it?? its like a guaranteed question on an exam sob

Reply 1

mqb2766

Original post by pharmacyrockz

i have watched so many youtube videos and my teachers explained it 34734398794 million times but i still cannot find the domain and ranges of functions and like graphs
could anyone idek have a way to acc understand and explain it?? its like a guaranteed question on an exam sob

It would probably be better to pick a single source (there are many, so just google for one you like) and work through it carefully and ask questions about it/the examples. Though a "simple" start would be
https://www.mathsisfun.com/definitions/domain-of-a-function.html

So, simply, the domain is the values that can go into a function (the x) and the range is what comes out (the y). So
y = x
both the natural domain and the range are all real values, though you could decide to restrict the domain to x>=0, and the corresponding range would be similar.
y = 1/x
has a natural domain of all real values except 0 (as the map is undefined when you divide by 0) and similarly for the range.
y = x^2
has a natural domain of all real values and the range is y>=0. However, when we talk about it being invertible we restrict the domain to x>=0 as then there is a one-to-one relationship and sqrt(x) maps positive values to positive values, so it is the inverse of x^2, when the domain of x^2 is the positive values.

Similarly for the trig functions like sin(x) and arcsin(x), so the domain of sin(x) is all real values (angles) and the range is -1<=y<=1. For sin() to be invertible (arcsin), we consider the domain of sin to be -pi/2<=x<=pi/2 (-90<=x<=90) and arcsin() has a corresponding domain and range.