# IB Mathematics (part-2)-Domain and Range of a function

In IB Mathematics 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

**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=**ℝ**-{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**

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