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. Solve the inequality for y. 2. Graph the corresponding equation as a boundary line. 3. Shade the appropriate region based on the inequality sign.

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 whether the parabola opens upwards or downwards.

Front

What is the general form of an absolute value function?

Back

y = a|bx - h| + k, where (h, k) is the vertex and 'a' determines the direction and width of the graph.

Front

How do you determine if you shade above or below the graph of an absolute value inequality?

Back

If the inequality is '≤' or '<', shade below the graph. If it is '≥' or '>', shade above the graph.

Front

What is the effect of the 'a' value in the function y = a|x - h| + k?

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 does the expression |x - h| represent?

Back

It represents the distance between x and h on the number line.

Front

How do you find the vertex of the function y = a|x - h| + k?

Back

The vertex is the point (h, k).

Front

What is the significance of the 'k' value in the function y = a|x - h| + k?

Back

The 'k' value represents the vertical shift of the graph; it moves the graph up if k > 0 and down if k < 0.

Front

How do you isolate y in an absolute value inequality?

Back

Rearrange the inequality to get y on one side, typically by adding or subtracting terms from both sides.