Question

on the coordinate grid, the graph of $y = \sqrt3{x - 1} + 3$ is shown. it is a translation of $y = \sqrt3{x}$. what is the domain of the graphed function? \\( \circ \\ \\{x \mid 1 < x < 5\\} \\) \\( \circ \\ \\{y \mid 1 < y < 5\\} \\) \\( \circ \\ \\{x \mid x \text{ is a real number}\\}\\) \\( \circ \\ \\{y \mid y \text{ is a real number}\\}\\)

Explanation:

Step1: Recall Domain Definition

Domain is all possible \( x \)-values of a function. So options with \( y \) (range) are eliminated (second, fourth options).

Step2: Analyze Cube Root Function

The function is \( y = \sqrt[3]{x - 1} + 3 \). Cube root of any real number is defined (no restriction like square root, which needs non - negative inside). So \( x - 1 \) can be any real number, meaning \( x \) can be any real number. The first option \( \{x|1 < x < 5\} \) is incorrect as there's no such restriction.

Answer:

\(\{x\mid x\text{ is a real number}\}\)