graphing absolute value inequalities

graphing absolute value inequalities

Assessment

Flashcard

Mathematics

9th Grade

Practice Problem

Hard

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Wayground Content

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that involves the absolute value of a variable expression, typically written in the form |expression| < c, |expression| > c, |expression| ≤ c, or |expression| ≥ c, where c is a constant.

2.

FLASHCARD QUESTION

Front

How do you graph an absolute value inequality?

Back

To graph an absolute value inequality, first graph the corresponding equation as a solid or dotted line depending on whether the inequality is inclusive (≤ or ≥) or exclusive (< or >). Then, shade the appropriate region above or below the line based on the inequality.

3.

FLASHCARD QUESTION

Front

What does it mean to shade above the line in a graph?

Back

Shading above the line in a graph indicates that the solutions to the inequality are greater than the values on the line. For example, for f(x) ≥ expression, you would shade above the line.

4.

FLASHCARD QUESTION

Front

What does it mean to shade below the line in a graph?

Back

Shading below the line in a graph indicates that the solutions to the inequality are less than the values on the line. For example, for f(x) ≤ expression, you would shade below the line.

5.

FLASHCARD QUESTION

Front

What is the difference between a solid line and a dotted line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (for ≤ or ≥ inequalities), while a dotted line indicates that the points on the line are not included (for < or > inequalities).

6.

FLASHCARD QUESTION

Front

How do you determine whether to use a solid or dotted line for an absolute value inequality?

Back

You use a solid line for inequalities that include equal to (≤ or ≥) and a dotted line for inequalities that do not include equal to (< or >).

7.

FLASHCARD QUESTION

Front

What is the general form of an absolute value inequality?

Back

The general form of an absolute value inequality is |ax + b| < c or |ax + b| > c, where a, b, and c are constants.

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