Q. 603 - Intermediate Algebra

Question

In the following exercise, ⓐ find the domain of the function ⓑ graph the function ⓒ use the graph to determine the range.

$g\left(x\right)=\sqrt{x+2}$

Step-by-Step Solution

Answer

The (a) domain of the function is $[-2,\infty )$

(b) The graph is shown in the figure

(c) The range of the function is $[0,\infty )$

Step 1. Given Information

$We have g\left(x\right)=\sqrt{x+2}$

Part (a) Step 1. Finding domain

Put $x+2\ge 0$

Simplify, we get $x\ge -2$

or in interval notation $[-2,\infty )$

Part (b) Step 1. Graph the function

To graph the function, we choose points in the interval [−2, ∞) that will also give us a radicand which will be easy to take the square root.

Part (c) Step 1. Finding Range

Looking at the graph, we see the y-values of the function are greater than or equal to zero. The range then is [0, ∞).