Question

Which of the following options does not represent a nonlinear function?

Answer 1

A linear function can be represented as $ymx+b$, where m represents the slope and b represents the $y-$intercept.
In $y=mx+b$, the power of the input is $1$.
So any function that can be written in this form or has the power of input as $1$ will be considered as a linear function.

Let us discuss each option.

$\to$ Surface area of a football, $S=4\pi r^2$ (where $r$ is radius of football)
Here $r$ is the input and $S$ is the output.
Let us compare the given function with the standard form of linear function.
Here, $S=4\pi r^2$ cannot be written in the form of $y=mx+b$, as power of input is $“2”$ in the given function.
So $S=4\pi r^2$ represents a nonlinear function.

$\to$ Area of an equilateral triangle photo frame, $A=\frac{\sqrt{3}}{4}{a}^2$ (where $a$ is the length of sides)
Here, $a$ is the input and A is the output.
Let us compare the given function with the standard form of linear function.
Here, $A=\frac{\sqrt{3}}{4}{a}^2$ cannot be written in the form of $y=mx+b$, as power of input is $“2”$ in the given function.
So $A=\frac{\sqrt{3}}{4}{a}^2$ represents a nonlinear function.
$\to$ Monthly electricity bill, $B=2p$ (where $p$ is the units of power consumption)
Here, $p$ is the input and $B$ is the output.
Let us compare the given function with the standard form of linear function.
Here $B=2p$ or $B=2p+0$ can be written in the form of $y=mx+b$, as power of input is $“1”$ in the given function.
$B=2p+0$
$\downarrow \downarrow \downarrow \downarrow$
$y=mx+b$,
$\to$ Area of a square lawn, $A=l^2$ (where $l$ is the length of sides)
Here, $l$ is the input and $A$ is the output.
Let us compare the given function with the standard form of linear function.
Here, $A=l^2$ cannot be written in the form of $y=mx+b$, as power of input is $“2”$ in the given function.
So $A=l^2$ represents a nonlinear function.

So option C is the correct answer.