Identifying the graphs of linear function — lesson. Mathematics State Board, Class 10.

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Graphs are an efficient way of visualizing 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:

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 an intercept

$c = 0$ and a slope

$m = 1$ is called an identity function.

The graphical representation of the 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 an intercept

$c = 0$ and slope

$m = -1$ is called an additive inverse function.

The graphical representation of the identity function is given by:

Important!

The linear functions are always one-to-one functions.

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4. Identifying the graphs of linear function