Graphing an absolute value inequality with a vertical shift

The video tutorial explains how to graph the inequality Y < |X + 5|. It begins by introducing the concept of absolute value inequalities and the parent graph Y = |X|. The tutorial then discusses the transformation caused by the '+5' and how it shifts the vertex of the graph. The instructor plots the new graph, ensuring it is represented as a dashed line since it is a 'less than' inequality. Finally, the video demonstrates how to test points to determine which areas of the graph are part of the solution set.

What is the parent graph of the inequality Y < |X + 5|?

• Y = X

• Y = |X|

• Y = X^2

• Y = |X + 5|

How does the addition of 5 affect the graph of Y = |X|?

• It moves the graph 5 units to the right.

• It moves the graph 5 units down.

• It moves the graph 5 units to the left.

• It moves the graph 5 units up.

Why is the graph represented as a dashed line?

• Because it is a 'greater than or equal to' inequality.

• Because it is a 'less than' inequality.

• Because it is a 'less than or equal to' inequality.

• Because it is a 'greater than' inequality.

Which test point is used to determine the solution region for the inequality?

• (-1,-1)

• (5,5)

• (0,0)

• (1,1)

What does it mean if the test point (0,0) satisfies the inequality?

• All points on the graph are solutions.

• All points below the graph are solutions.

• All points outside the graph are solutions.

• All points above the graph are solutions.