# Graphs of Functions

## A relation f from a set A to set B is said to be a function if every element of set A has one and only one image in set B.Vertical line test is used to determine if a relation is a function or not. A relation is a function if vertical lines intersect the graph only at one point.Let A and B be two non-empty sets. Then, a function ‘f’ from set A to set B is a rule or a method that associates the elements of set A with the elements of set B such that:1. All the elements of set A are associated with the elements of set B.2. An element of set A is associated with a unique element in set B.Graphs are the geometrical visualisation of functions. Therefore, they help us to understand the domain, range and other information about the function.Graph of a real function ‘f’, denoted by G (f) is the set of all ordered pairs {x, f(x)} of real numbers where x belongs to the domain of f.Keywords: Identity functions, Constant functions, Modulus functions, Greatest integer functions, Signum functions, Reciprocal functions, Rational functions, Polynomial functions, Logarithmic functions, Exponential functions

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• Q1

Marks:1

##### Explanation:

k(x) is not an exponential function because the independent variable must appear in the exponent for the function to be exponential function.

• Q2

Marks:1

intersects the y-axis

• Q3

Marks:1

• Q4

Marks:1

##### Explanation:

Critical points are x = 1, 2, 3.