Find the Domain and Range y=(2x^2+5x-3)/(x+3)

$y = \frac{2 x^{2} + 5 x - 3}{x + 3}$

Set the denominator in $\frac{2 x^{2} + 5 x - 3}{x + 3}$ equal to $0$ to find where the expression is undefined.

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

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

Interval Notation:

$(- \infty, - 3) \cup (- 3, \infty)$

Set-Builder Notation:

${x | x \neq - 3}$

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

Interval Notation:

$(- \infty, - 7) \cup (- 7, \infty)$

Set-Builder Notation:

${y | y \neq - 7}$

Determine the domain and range.

Domain: $(- \infty, - 3) \cup (- 3, \infty), {x | x \neq - 3}$

Range: $(- \infty, - 7) \cup (- 7, \infty), {y | y \neq - 7}$