Mathematics, 11.10.2019 04:20 tatyanaknight122

Me and show step by step and show your this is due tomorrow and this is my last time asking

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Answer from: xdimplesjoon

see below

Step-by-step explanation:

The "work" consists of understanding what you're reading when you read the inequality.

In each case, the parent function is the absolute value function. This is something you should be familiar with. In case you're not, a graph of it is shown in the 3rd attachment.

In the different inequalities, the absolute value function has been vertically scaled, translated downward, and translated to the right. These transformations are easy to read when you know what to look for.

When the parent function is multiplied by a factor, such as "k" in ...

y = k·|x|

that represents a vertical scale factor. In the case of the graph of the absolute value function, it will be the slope of the lines. In this case, where there is no translation of the function, for values of x > 0, the slope is k; for values of x < 0, the slope is -k. In problem 11, k=1/2, so the slopes of the lines on the graph will be ±1/2.

If the scale factor is negative, the function is reflected across the x-axis. You see this in problem 12.

When something is subtracted from x, as in problem 12, where you have |x-3|, that value is a horizontal translation to the right. In this problem, the absolute value function is translated 3 units to the right. (The negative scale factor shows it is also reflected across the x-axis, so opens downward instead of upward.)

When something is subtracted from the function value, as in |x|-4, that something represents a translation downward. You see this in problem 11.

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11. The absolute value function is vertically scaled by a factor of 1/2 and translated downward 4 units. The vertex will be at (0, -4) and the boundary lines will extend upward from there 1 unit for each 2 units left or right from the vertex.

Because the inequality is strictly "greater than", the boundary lines are graphed as dashed lines. The "greater than" means the shading will be above the (dashed) line, where values of y are greater than those on the line.

12. The absolute value function is not scaled, but is reflected across the x-axis and translated 3 units to the right. It will have a "rise" of -1 for each unit to the left or right of the vertex at (3, 0).

Because the inequality is strictly "less than", the boundary lines are graphed as dashed lines. The "less than" means shading will be below the (dashed) boundary line, where values of y are less than those on the line.