Graphing Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An inequality that contains an absolute value expression, typically in the form |x| < a or |x| > a.

Front

How do you graph an absolute value inequality?

Back

1. Graph the corresponding absolute value equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the appropriate region based on the inequality.

Front

What does the vertex of an absolute value function represent?

Back

The vertex is the highest or lowest point of the graph, depending on the direction it opens.

Front

What is the vertex of the function y = 2|x - 3| + 1?

Back

(3, 1)

Front

How does the coefficient of the absolute value affect the graph?

Back

A positive coefficient makes the graph open upwards, while a negative coefficient makes it open downwards.

Front

What is the effect of adding a constant outside the absolute value?

Back

It shifts the graph vertically. For example, y = |x| + 3 shifts the graph up by 3 units.

Front

What does the inequality y > -2|x| + 4 represent?

Back

It represents the region above the line y = -2|x| + 4.

Front

How do you determine if a point is a solution to an absolute value inequality?

Back

Substitute the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the difference between |x| < a and |x| > a?

Back

|x| < a means x is within a distance a from 0, while |x| > a means x is outside that distance.

Front

What does the graph of y = -2|x - 3| + 5 look like?

Back

It is a downward-opening V-shape with vertex at (3, 5).