Question

PLEASE ANSWER THESE QUICK I NEED HELP PLEASE ITS ALGEBRA

Answer 1

Step-by-step explanation:

1.)  y = - |x - 4| - 5 is an absolute value graph, where its vertex occurs at point (4, -5). The general form of the absolute value function is y = a |x – h| + k, where where:

• a ≠ 0, and the value of a determines whether the graph opens up or down. If a is between 0 and 1, the graph is wider than the parent function.
• (h, k ) represents the vertex.

The given absolute value function, y = - |x - 4| - 5 is a downward-facing graph, where it is translated 4 units to the right (as given by the value of h = 4), and 5 units downward (as given by the value of k = 5).  

2.) The Vertical Line Test allows us to know whether or not a graph is actually a function.  If a vertical line intersects the graph in all places at exactly one point, then the relation is a function. To use the vertical-line test, imagine dragging a ruler held vertically across the  graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value.  If you do this for the given graph, every vertical line intersects the graph in at most one point.

Attached is the graph of the given function, where I performed the Vertical Line Test.  As evidenced in the graph, every green vertical line intersects the graph at exactly one point (red dots on the graph). Thus, the graph passed the Vertical Line Test, thereby qualifying as a function.  

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