Algebra Examples

$\frac{4 x}{x - 9} = y$

Step 1

Rewrite the equation as $y = \frac{4 x}{x - 9}$ .

$y = \frac{4 x}{x - 9}$

Step 2

Set the denominator in $\frac{4 x}{x - 9}$ equal to $0$ to find where the expression is undefined.

$x - 9 = 0$

Step 3

Add $9$ to both sides of the equation.

$x = 9$

Step 4

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

Interval Notation:

$(- \infty, 9) \cup (9, \infty)$

Set-Builder Notation:

${x | x \neq 9}$

Step 5

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

Interval Notation:

$(- \infty, 4) \cup (4, \infty)$

Set-Builder Notation:

${y | y \neq 4}$

Step 6

Determine the domain and range.

Domain: $(- \infty, 9) \cup (9, \infty), {x | x \neq 9}$

Range: $(- \infty, 4) \cup (4, \infty), {y | y \neq 4}$

Step 7