Domain And Range

Not every function has to be infinite. For certain functions, you may indicate boundries, at which the function will end for both x and y axes. For instance, let's suppose we have the linear function:

f(x)=x

Then we may a note the limit of the function by adding the following to our function notation:

D(∞, ∞) and R(∞, ∞)

D stands for domain, which is the start and end points on the horizontal (x) axis. R stands for range which is the start and end point of the vertical (y) axis.

The reason for using the infinite symbol is because our linear function goes infinitely horizontally, and infinitely vertically, if it would stop at a certain point on our graph, we may include the numbers where the function starts and ends. 

In the case of an infinite function, you can write both the domain and range with the following notation as well:

D: x ∈  ℝ

R: y ∈  ℝ

Which essentially means that x and y are elements of two real numbers (ℝ). (You don't need to worry about non-real numbers for Mathematics AA SL.) NOTE that this notation works for infinite functions only not finite.

This is also a possible notation for domain and range:

D: ∞ ≤ x ≤ ∞

R: ∞ ≤ y ≤ ∞

In the IB Diploma Programme, all three notations are accepted. 

But what if the function is finite with boundries? Check the worked example section where we explain step by step.

The function of g is shown by (fig 5.0). Find the domain of the function. 

The domain is the horizontal axis. 

The graph of g starts at point -1 and stops at point 5. Hence the notation is -1 ≤ x ≤ 5.

So the answer is

 -1 ≤ x ≤ 5.