Ohio Assessments for Educators (OAE) Mathematics Practice Exam 2025 - Free Practice Questions and Study Guide

The domain of the function \( f(x) = \sqrt{ax + b} \) is determined by the requirement that the expression inside the square root must be non-negative. This is because the square root function is only defined for non-negative numbers in the real number system.

To find the domain, you set up the inequality:

\[ ax + b \geq 0. \]

This means that we need to solve this inequality to find the values of \( x \) for which it holds true. The solution set will provide the values of \( x \) that keep the expression inside the square root non-negative, which is crucial for the output of the function to be real numbers.

Therefore, the domain of \( f(x) = \sqrt{ax + b} \) is given by the values of \( x \) that satisfy \( ax + b \geq 0 \). This requirement characterizes option B accurately, as it specifically points out that the function is defined for all real numbers where the expression \( ax + b \) is greater than or equal to zero. The other options do not appropriately reflect this fundamental requirement for defining the domain of the square root function.