Question

Match the following

• A. Non-linear function
• B. Linear function
• C. Non-linear function
• D. Non-linear function

Answer 1

$y=8x+3$ is a linear function.
As $y=8x+3$ can be written as $y=8x^1+3x^0$
We know that a function having the exponents of $x$ as $0$ or $1$ is a linear function.
Here in $y=8x+3$ the exponent of $x$ are $1$ and $0$. Hence $y=8x+3$ is a linear function.

$y=2x^2-6x+8$ is not a linear function.
$y=2x^2-6x+8$ can be written as $y=2x^2-6x^1+8x^0$
We know that a function having the exponents of x as 0 or 1 is a linear function.
Here in $2x^2-6x+8$ the exponent of x are 2, 1 and 0. Hence $y=$ is not a linear function.

$y=\frac{4}{x}$ is not a linear function.
$y=\frac{4}{x}$ can be written as $y=4x^{-1}$
We know that a function having the exponents of x as 0 or 1 is a linear function.
Here in $y=\frac{4}{x}$ the exponent of x is -1. Hence $y=\frac{4}{x}$ is not a linear function.

$y=x+x^{\frac{1}{4}}$ is not a linear function.
$y=x+x^{\frac{1}{4}}$ can be written as $y=x^1+x^{\frac{1}{4}}$
We know that a function having the exponents of x as 0 or 1 is a linear function.
Here in $x+x^{\frac{1}{4}}$ the exponent of x are 1 and $\frac{1}{4}$. Hence $x+x^{\frac{1}{4}}$ is not a linear function.