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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****Additive inverse 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:

*Additive inverse function*:

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.