12.5 - Graphing Absolute Value Inequalities

Front

What is an absolute value inequality?

Back

An inequality that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you graph an absolute value inequality?

Back

1. Graph the corresponding absolute value equation as a boundary line. 2. Determine if the inequality is strict (< or >) or inclusive (≤ 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 point where the graph changes direction, and it represents the minimum or maximum value of the function.

Front

For the inequality f(x) ≤ |x| + 1, where do you shade?

Back

Below the line.

Front

What is the general form of an absolute value function?

Back

f(x) = a|bx - h| + k, where (h, k) is the vertex.

Front

What does the 'a' in the absolute value function affect?

Back

The 'a' value affects the vertical stretch or compression and the direction of the graph (upward if a > 0, downward if a < 0).

Front

What is the effect of changing 'h' in the function f(x) = |x - h|?

Back

Changing 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What is the effect of changing 'k' in the function f(x) = |x| + k?

Back

Changing 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

How do you determine the shading direction for y > |x| + 2?

Back

Shade above the line.

Front

What is the solution set for the inequality |x| < 3?

Back

-3 < x < 3.