Exploring Absolute Value Inequalities in Graphs

This video tutorial covers two-variable absolute value inequalities, focusing on graphing techniques and transformations. It includes examples of horizontal, vertical, rightward, and downward transformations, as well as reflecting and stretching graphs. The tutorial also explains how to write inequalities from graphs, emphasizing the importance of identifying vertex locations and understanding shading in relation to the V-shape of the graph.

What is the primary goal when working with two-variable absolute value inequalities?

• To isolate the x variable

• To isolate the y variable

• To eliminate the absolute value

• To find the vertex

In the first inequality, what does the horizontal translation of 6 units to the left indicate?

• The graph shifts 6 units upwards

• The graph shifts 6 units downwards

• The graph shifts 6 units to the right

• The graph shifts 6 units to the left

What does the vertical compression factor of one-half do to the graph?

• Shifts the graph horizontally

• Compresses the graph vertically

• Reflects the graph

• Stretches the graph vertically

In the second inequality, what does the subtraction of 4 from x inside the absolute value indicate?

• A downward translation by 4 units

• An upward translation by 4 units

• A rightward translation by 4 units

• A leftward translation by 4 units

What does the subtraction of 5 outside the absolute value indicate in the second inequality?

• An upward translation by 5 units

• A rightward translation by 5 units

• A leftward translation by 5 units

• A downward translation by 5 units

In the third inequality, what does multiplying by a negative do to the inequality symbol?

• Doubles it

• Eliminates it

• Changes its direction

• Keeps it the same

What does the negative sign in front of the absolute value indicate in the third inequality?

• Shifts the graph upwards

• Reflects the graph in the x-axis

• Shifts the graph downwards

• Reflects the graph in the y-axis

In the fourth inequality, what does the rightward shift of 1 unit indicate?

• The graph shifts 1 unit upwards

• The graph shifts 1 unit to the right

• The graph shifts 1 unit to the left

• The graph shifts 1 unit downwards

What does the upward shift of 7 units indicate in the fourth inequality?

• The graph shifts 7 units upwards

• The graph shifts 7 units downwards

• The graph shifts 7 units to the right

• The graph shifts 7 units to the left

When writing an absolute value inequality from a graph, what is the first thing to identify?

• The y-intercept

• The x-intercept

• The vertex

• The slope