Find the Domain and Range y = log base 7 of x-2+3

$y = \log_{7} (x - 2) + 3$

Set the argument in $\log_{7} (x - 2)$ greater than $0$ to find where the expression is defined.

$x - 2 > 0$

Add $2$ to both sides of the inequality.

$x > 2$

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

Interval Notation:

$(2, \infty)$

Set-Builder Notation:

${x | x > 2}$

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

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Determine the domain and range.

Domain: $(2, \infty), {x | x > 2}$

Range: $(- \infty, \infty), {y | y \in ℝ}$