Understanding Absolute Value Concepts

Professor Dave introduces absolute values, explaining their definition as the distance from zero on a number line. He discusses properties of absolute values, such as how they affect multiplication and division, but not addition. The video covers solving equations with absolute values, demonstrating how to find multiple solutions. Finally, it explains graphing absolute value functions, showing how negative inputs are reflected to form a V-shaped graph.

What is the absolute value of a number primarily defined as?

• The negative of the number

• The distance from zero on a number line

• The number itself

• The square of the number

How does the absolute value affect negative numbers?

• It squares them

• It leaves them unchanged

• It makes them positive

• It doubles the number

Which of the following is true about the absolute value of a product?

• It is the absolute value of the difference

• It is the product of the absolute values

• It is the absolute value of the sum

• It is the sum of the absolute values

What happens when you add absolute values of two numbers?

• It does not equal the absolute value of their sum

• It is always zero

• It equals the absolute value of their difference

• It equals the absolute value of their sum

If the absolute value of X is 2, what are the possible values of X?

• 0 and 2

• 2 and -2

• Only 2

• Only -2

How do you solve the equation |2X - 1| = 5?

• By subtracting 5 from both sides

• By finding one solution

• By solving two separate equations

• By adding 5 to both sides

What is the shape of the graph of Y = |X|?

• A straight line

• A circle

• A V-shape

• A parabola

How does the graph of Y = |X| differ from Y = X?

• It is a straight line

• It is a vertical line

• It is a horizontal line

• It reflects negative values across the X-axis

What happens to negative X values in the graph of Y = |X|?

• They are reflected to positive Y values

• They become zero

• They remain negative

• They are doubled

What is the Y-intercept of the graph Y = X?

• 0

• 1

• -1

• 2