Question

Which description matches the graph of the inequality y > |x + 4| – 1? a shaded region above a solid boundary line a shaded region above a dashed boundary line a shaded region below a dashed boundary line a shaded region below a solid boundary line

Answer 1

The description that matches the graph of the inequality y > |x + 4| – 1 is a shaded region above a solid boundary line.

The answer is option ⇒1

Explanation:

The correct answer is 1. a shaded region above a solid boundary line.

To understand the graph of the inequality y > |x + 4| – 1, let's break it down into steps.

1. The expression |x + 4| represents the absolute value of (x + 4). The absolute value function always gives a non-negative value.

2. The expression |x + 4| – 1 represents the absolute value of (x + 4) minus 1.

3. The inequality y > |x + 4| – 1 means that y is greater than the value obtained by evaluating |x + 4| – 1 for different values of x.

4. To graph this inequality, we start by graphing the equation y = |x + 4| – 1. This equation represents the boundary line of the inequality.

5. The boundary line is a solid line because the inequality is strict (y >). This means that the points on the boundary line are not included in the shaded region.

6. The shaded region above the solid boundary line represents the values of y that are greater than |x + 4| – 1. This is because the inequality states that y is greater than the value obtained from the absolute value function.

Therefore, the description that matches the graph of the inequality y > |x + 4| – 1 is 1. a shaded region above a solid boundary line.

The answer is option ⇒1

Answer 2

The correct option is:

Shaded region above dashed boundry line.

Explanation:

The question is incomplete as the graphs are not given. Lets make the graph of the given function and you can match it with the options to see which is the solution.

We have been given the function:

y > |x + 4| - 1

This can be divided into two equations:

y > (x + 4) - 1 , y > -(x + 4) -1

Simplify both equations.

y > x + 4 - 1 , y > -x - 4 - 1

y > x + 3 , y > -x - 5

Graph both equations

The red region shows the first equation, the green region shows the second equation. The brown region satisfies the inequality.

Compare it with your graph to get the answer, i think it should shaded region above dashed boundry line