Domain: $(-5, 0]$ Range: $[-3, 3)$
Work Step by Step
Some important observations about the graph: (i) The lowest point is at $(0, -3)$. (ii) The highest point, though it is not really part of the graph since a hole (hollow dot) was used, is at $(-5, 3)$. (iii) The graph is decreasing from left to right. The domain is the set that contains all the x-values of a function. The x-values of the given function vary from any number greater than $-5$ (-5 is not included because a hollow dot or a hole was used to plot the point (-5, 3)) up to $x=0$. Thus, the domain of the given function is $(-5, 0]$. The range of a function is the set of y-values. Notice that the y-values covered by the graph vary from $y=-3$ up to any number less than 3 (3 is not included because a hollow dot or a hole was used to plot the point (-5, 3)). Thus, the range of the function is $[-3, 3)$.