Find the Domain and Range f(x)=(22+x)/(25+x)

$f (x) = \frac{22 + x}{25 + x}$

Step 1

Set the denominator in $\frac{22 + x}{25 + x}$ equal to $0$ to find where the expression is undefined.

$25 + x = 0$

Step 2

Subtract $25$ from both sides of the equation.

$x = - 25$

Step 3

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

Interval Notation:

$(- \infty, - 25) \cup (- 25, \infty)$

Set-Builder Notation:

${x | x \neq - 25}$

Step 4

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

Interval Notation:

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

Set-Builder Notation:

${y | y \neq 1}$

Step 5

Determine the domain and range.

Domain: $(- \infty, - 25) \cup (- 25, \infty), {x | x \neq - 25}$

Range: $(- \infty, 1) \cup (1, \infty), {y | y \neq 1}$

Step 6