Absolute Value Inequality Graphs

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that involves the absolute value of a variable expression, indicating the distance of the expression from zero on a number line.

Front

How do you graph the inequality y > |x|?

Back

To graph y > |x|, plot the V-shaped graph of y = |x|, then shade the region above the graph, indicating all points where y is greater than |x|.

Tags

CCSS.HSA.REI.D.12

Front

What does the graph of y < |x + 2| look like?

Back

The graph of y < |x + 2| is a V-shaped graph shifted 2 units to the left, with the area below the graph shaded.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the vertex in absolute value graphs?

Back

The vertex is the point where the graph changes direction; it represents the minimum or maximum value of the function.

Tags

CCSS.HSF-IF.C.7D

Front

How do you solve the inequality y > -|x + 2| + 2?

Back

To solve y > -|x + 2| + 2, first graph y = -|x + 2| + 2, then shade the area above the graph.

Front

What does the inequality y < -|x + 3| - 2 represent?

Back

This inequality represents the area below the graph of y = -|x + 3| - 2, which is a downward-opening V shape.

Front

How do you determine the solution set for y > -|x + 2| - 3?

Back

The solution set includes all points above the graph of y = -|x + 2| - 3.

Front

What is the general form of an absolute value inequality?

Back

The general form is |expression| < or > constant, where 'expression' is a linear function of x.

Front

How do you find the critical points of an absolute value inequality?

Back

Critical points are found by setting the expression inside the absolute value equal to zero and solving for x.

Front

What is the effect of changing the sign in front of the absolute value?

Back

Changing the sign in front of the absolute value flips the graph vertically, affecting the direction of the inequality.

Tags

CCSS.HSF-IF.C.7A