Problem 13 - Algebra 1: Concepts and Skills

Question

Find the domain and the range of the function. $$y=\sqrt{x+5}$$

Step-by-Step Solution

Answer

The domain of the function is \(x\geq -5\) and the range of the function is \(y\geq 0\)

Step 1: Determine the Domain

The domain of a function consists of all possible input values. For a square root function, such as this one, the expression under the square root (the radicand) must be greater than or equal to zero, because the square root of a negative number doesn't result in a real number. Hence we get the inequality: \(x+5\geq 0\) . Solve this inequality for x which gives \(x\geq -5\). So the domain of the function is all real numbers greater than or equal to -5.

Step 2: Determine the Range

The range of a function contains all possible output values. For a square root function, this represents possible values of y. Since taking the square root doesn't result in negative values, the range of a square root function is always greater than or equal to zero (as long as the domain doesn't restrict it further). Hence the range of the function is \(y\geq 0\).