### Theory:

Graphs are an efficient way of visualizing the curves and functions.

Let us discuss how to identify the graphs of a linear function.
Linear function:
A function $$f: \mathbb{R} \rightarrow \mathbb{R}$$ defined by $$f(x) = mx + c$$, $$m \neq 0$$ is called a linear function.
The graph of a linear function simply represents a straight line.

Let us further discuss some specific linear functions.

• Identity function

Identity function:
A function $$f: \mathbb{R} \rightarrow \mathbb{R}$$ defined by $$f(x) = x$$, is called an identity function.
In other words, a linear function having the intercept $$c = 0$$ and slope $$m = 1$$ is called an identity function.

The graphical representation of identity function is given by:

A function $$f: \mathbb{R} \rightarrow \mathbb{R}$$ defined by $$f(x) = - x$$, is called an additive inverse function.
In other words, a linear function having the intercept $$c = 0$$ and slope $$m = -1$$ is called an additive inverse function.

The graphical representation of identity function is given by:

Important!
The linear functions are always one-one functions.