NBCT Mathematics Adolescence And Young Adulthood (AYA) Component 1 Practice Test

What are the domain and range of f(x) = sqrt(x - 2)?

Domain x ≥ 2; Range y ≥ 0. Domain x > 2; Range y > 0. Domain x ≥ 0; Range y ≥ 0. Domain x ≤ 2; Range y ≤ 0.

Correct Answer:

Domain x > 2; Range y > 0.

Explanation:

The main idea is that a square root requires the inside quantity to be nonnegative, and the result is always nonnegative as well. For f(x) = sqrt(x - 2), the inside is x - 2, so we need x - 2 ≥ 0, which means x ≥ 2. When x = 2, f(x) = sqrt(0) = 0, so 0 is included in the range. As x grows, x - 2 grows and the square root grows as well, giving all nonnegative values. So the domain is all x with x ≥ 2, and the range is all y with y ≥ 0. The choice that would exclude x = 2 or require the output to be negative isn’t correct, and the one that starts above 0 would miss the value at x = 2.

Access more questions from this quiz

Continue to NBCT Mathematics Adolescence and Young Adulthood (AYA) Component 1 Practice Test for more practice questions and the full quiz experience.

Access More Questions