Understanding Absolute Value

What is the definition of absolute value?

• The absolute value of a number is its non-negative value without regard to its sign.

• The absolute value of a number is its negative value.

• The absolute value is the original number without any changes.

• The absolute value is the square of a number.

How do you graph the function y = |x|?

• The graph of y = |x| is a circle centered at the origin.

• The graph of y = |x| is a straight line with a slope of 1.

• The graph of y = |x| is a parabola that opens downwards.

• The graph of y = |x| is a V-shaped graph that opens upwards with the vertex at the origin.

Solve the equation |x - 3| = 5.

• x = 10

• x = 8, x = -2

• x = 3

• x = -5

What are the solutions to the inequality |x + 2| < 4?

• (-8, -4)

• (2, 6)

• (-6, 2)

• (-4, 0)

Give an example of a real-world application of absolute value.

• Determining the time taken for a journey.

• Calculating the area of a triangle.

• Calculating distances between points on a number line.

• Measuring temperature in Celsius.

If the distance between two points is 7, what is the absolute value of their difference?

• 7

• 5

• 10

• 3

How do you solve the equation |2x + 1| = 3?

• x = -1

• x = 0

• x = 2

• x = 1 or x = -2

What does the graph of y = |x - 1| look like?

• A U-shaped graph with a vertex at (1, 1) that opens downwards.

• A horizontal line at y = 1.

• A V-shaped graph with a vertex at (1, 0) that opens upwards.

• A straight line with a slope of 1.

Explain how absolute value relates to distance on a number line.

• Distance on a number line is always negative.

• Absolute value measures the size of a number only.

• Absolute value indicates distance from zero on a number line.

• Absolute value is irrelevant to number lines.

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

• (-∞, 3)

• (-∞, -3] ∪ [3, ∞)

• [3, ∞)

• [-3, 3]