Find the Domain and Range f(x)=(3x-6)/x+4.5

$f (x) = \frac{3 x - 6}{x} + 4.5$

Step 1

Set the denominator in $\frac{3 x - 6}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2

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

Interval Notation:

$(- \infty, 0) \cup (0, \infty)$

Set-Builder Notation:

${x | x \neq 0}$

Step 3

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

Interval Notation:

$(- \infty, \frac{15}{2}) \cup (\frac{15}{2}, \infty)$

Set-Builder Notation:

${y | y \neq \frac{15}{2}}$

Step 4

Determine the domain and range.

Domain: $(- \infty, 0) \cup (0, \infty), {x | x \neq 0}$

Range: $(- \infty, \frac{15}{2}) \cup (\frac{15}{2}, \infty), {y | y \neq \frac{15}{2}}$

Step 5