Answer
The graph representing the function is provided below. Here’s a step-by-step breakdown: The base absolute function can be defined as g(x)=|x|, which forms a V-shape with its vertex located at the origin. The function we are looking at is [tex]f(x)=-|x|-2[/tex] ………… (1) The vertex form for an absolute function is [tex]f(x)=a|x-h|+k[/tex] ………… (2), where a is a constant and (h,k) indicates the vertex. From equations (1) and (2), we deduce that [tex]a=-1,h=0,k=-2[/tex]. Since a is negative, it implies the graph of the parent function is reflected over the x-axis. The vertex (0,-2) signifies that the graph of the parent function is translated 2 units downwards. The graph corresponding to the specified function is displayed below.
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