Q6. - Algebra 1

Question

State the excluded value for the function.

$\mathit{y}\mathbf{=}\frac{\mathbf{2}}{\mathbf{x}}$

Step-by-Step Solution

Answer

The excluded value for the function $y=\frac{2}{x}$ is $\mathit{x}\mathbf{=}\mathbf{0}$.

Step 1. Define a rational function.

A function of the form $y=\frac{p}{q}$ is called a rational function, where $p$ and $q$ are the polynomials and $q\ne 0$.

Step 2. Define quotient of power rule.

The quotient of power rule is given by

$\frac{a^m}{a^n}=a^{m-n}$

Where, is any non-zero real number.

Step 3. Define the excluded values for the rational function.

Any value of a variable that results in a denominator of zero in a rational function is excluded from the domain of the function and these values are called the excluded values of the rational function.

Step 4. Simplify the expression 16 x 2 y 3 8 x y .

Use quotient of power rule to simplify the expression .

Denominator $=0$

$x=0$

Therefore the excluded value for the function $y=\frac{2}{x}$ is $x=0$.