Find the Domain and Range (x^2)/(x-1)

$\frac{x^{2}}{x - 1}$

Set the denominator in $\frac{x^{2}}{x - 1}$ equal to $0$ to find where the expression is undefined.

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, 1) \cup (1, \infty)$

Set-Builder Notation:

${x | x \neq 1}$

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, 0] \cup [4, \infty)$

Set-Builder Notation:

${y | y \leq 0, y \geq 4}$

Determine the domain and range.

Domain: $(- \infty, 1) \cup (1, \infty), {x | x \neq 1}$

Range: $(- \infty, 0] \cup [4, \infty), {y | y \leq 0, y \geq 4}$