Question

Which of the following graphs represent a linear function (over its whole domain)?

• A. $\left(1\right),\left(2\right),\left(3\right)$ and $\left(4\right)$
• B. Only $\left(1\right),\left(2\right)$ and $\left(3\right)$
• C. Only $\left(1\right)$ and $\left(2\right)$
• D. Only $\left(2\right)$

Answer 1

The correct option is C Only $\left(1\right)$ and $\left(2\right)$

Linear function is of the form $f\left(x\right)=ax+b$
where $a$ is any constant term and $a\in R$
Graph of linear function is a straight line.


It is a special case of linear function, when $f\left(x\right)=ax+b$ and $a=0$
It is a linear function.


It is clearly a linear function.
$f\left(x\right)=ax+b$


Clearly, the graph is not a straight line for all $x\in R$
So, it is not a linear function.


By vertical line test, we can prove that it is not a function.
So, it is not a linear function.