Graph the inequality y < –|x – 4|. Which point is NOT part of the solution?
The question makes no sense.
There are an infinite number of points which are not part of the solution.
Here is what the graph looks like
http://www.wolframalpha.com/input/?i=plot+y+%3C+%E2%80%93%7Cx+%E2%80%93+4%7C
when x=4, y<-0 which is a questionable use of zero. IEEE standard in computing allows zero with signs as an aid to computing, but in ordinary computation, it has no meaning. y being less than something with no meaning is questionable.
To graph the inequality y < -|x - 4|, we can start by graphing the equation y = -|x - 4| and then shade the area below the graph.
To graph y = -|x - 4|, we can break it down into two cases:
1. When x - 4 is positive, meaning x > 4
In this case, the equation becomes y = -(x - 4) or y = -x + 4.
We can graph this linear equation as a straight line with a y-intercept of 4 and a negative slope of -1.
2. When x - 4 is negative, meaning x < 4
In this case, the equation becomes y = -(4 - x) or y = x - 4.
We can graph this linear equation as a straight line with a y-intercept of -4 and a positive slope of 1.
The graph of y = -|x - 4| consists of two lines, y = -x + 4 and y = x - 4, that intersect at point (4, 0) and create a "V" shape.
To represent the inequality y < -|x - 4|, we shade the area below the "V" shape graph. The shading indicates that any point below the "V" shape is part of the solution.
Now, let's identify the point that is NOT part of the solution.
Since all the points below the "V" shape graph are part of the solution, the point (4, 0) is NOT part of the solution because it lies on the boundary of the inequality, y = -|x - 4|.
Therefore, (4, 0) is the point that is NOT part of the solution to the inequality y < -|x - 4|.
To graph the inequality y < –|x – 4|, we need to follow a few steps:
Step 1: Graph the boundary line
The inequality involves an absolute value, so we start by creating the boundary line. The expression inside the absolute value, x – 4, equals zero when x = 4. Thus, the boundary line is a vertical line passing through x = 4.
Step 2: Determine the inequality sign
Since the inequality is y < –|x – 4|, we know that the solution lies below the boundary line.
Step 3: Find test points
To determine which region satisfies the inequality, we can choose test points in each region.
Let's consider two test points, the point (3, 0) and the point (5, 0). Substitute these points into the inequality to see if they satisfy it:
For the point (3, 0):
0 < –|3 – 4|
0 < –|-1|
0 < –1 (False)
For the point (5, 0):
0 < –|5 – 4|
0 < –|1|
0 < –1 (False)
Both test points don't satisfy the inequality, which means that the region below the boundary line is not part of the solution.
Step 4: Graph the solution
Based on the test points, we can conclude that the solution consists of the region above the boundary line. We shade the area above the vertical line passing through x = 4.
So, to answer your question, every point above the vertical line passing through x = 4 is part of the solution. None of these points are excluded.