Problem 14 - Algebra 1: Concepts and Skills

Question

Find the domain and the range of the function. $$y=\sqrt{x-10}$$

Step-by-Step Solution

Answer

The domain of the function is \(x \geq 10\) and the range is \(y \geq 0\).

Step 1: Find the Domain

The function is only defined when the value under the square root is nonnegative. Therefore, you set the value inside the square root greater than or equal to 0 and solve for \(x\). So, to find the domain, we have \(x - 10 \geq 0\). Solving for \(x\) gives \(x \geq 10\).

Step 2: Find the Range

The square root function will always output nonnegative numbers. This is because a square root of a number is a value which, when multiplied by itself, gives the original number. Since we cannot have a negative result when we multiply two equal values, the square root function can only output nonnegative numbers. In this case, \(y = \sqrt{x - 10}\) will output all values \(y \geq 0\) because all nonnegative numbers have real square roots.