For IB Maths Tutors both HL and SL, functions are one of the most important areas because they lie at the heart of much of mathematical analysis.here I am discussing domain and range of a function

Domain of a Function

Suppose I say that f is a real function.This means that for real input, the output should be real. For example

F(x)=√x

if F is real, then x can only take non-negative values because only then the output will be real. Set of all real values of R is called domain

“Domain is the set of all possible inputs for which the output is real ”

In some cases, x is defined explicitly. for example,

y=f(x)

=x²;    1<x>2 here domain is defined explicitly as (1,2)

If no domain is mentioned explicitly, the domain will be assumed to be such that “F” produces real output

These are a few examples

1. y=f(x)=√x
Domain D= x≥0

2)           f(x)=√x

Domain   D= 2∠x≤3      or     x∈(2,3)

3)         y=1∕x  then domain will be any real number excluding zero

Domain D=-{0}

4)        y=logx  then the domain will be any positive integer because logs are only defined for positive real numbers

D=x≥1
Range of a function- It is simply the set of possible outputs for a defined domain.

Range depends upon domain
Examples:

1)  y=x²

Domain  x=ℝ

Range    y≥0

2)  y=√x

Domain x≥0

Range    y≥0

3)  y=√x            2∠x≤3

Domain  x=(2,3)

Range     y=(√2,√3)

Question asked in IB Mathematics are usually more complex than above examples

To have a graphical picture in mind, consider this image

When plotted on a graph, the independent variable (x) is plotted on the horizontal axis while the dependent variable (y) is plotted on vertical axis

Suppose y depends on x as shown in above figure. You can easily tell the domain and range of the function just by looking at the above figure.
Domain D=a≤x≤b or

D=[a,b]

look along the y axis and we see that the graph only varies only between certain values of y

so Range R=c≤x≤d or

R=[c,d]

To summarise, for domain look along x-axis, for range look along y-axis

Try these questions and find domain and range of a function.pdf

In my next article on IB Mathematics, I will discuss various types of functions