Problem 11 - 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 \(x \geq 0\) and the range is \(y \geq -10\).

Step 1: Find the domain

For the given function, the square root is only defined for values greater than or equal to 0. Therefore, the domain of the function is \(x \geq 0\). This means that any value of x that is greater than or equal to 0 is included in the domain.

Step 2: Find the range

To find the range of the function, consider the minimum and maximum values that y can take given the domain. Since the smallest value of \(x\) is 0, the smallest value of \(y\) will be \(\sqrt{x}-10\) which becomes \(\sqrt{0}-10\), or -10. As \(x\) increases, \(y\) increases as well. Therefore, the range includes all numbers greater than or equal to -10.