Understanding Absolute Value Functions

The video tutorial explains how to solve a hot air balloon problem using absolute value functions. It begins with an introduction to the problem and the function representing the balloon's height. The lesson reviews the concept of absolute value, addressing common misunderstandings. It then demonstrates how to graph absolute value functions using a t-table and transformations. The tutorial concludes by solving the hot air balloon problem, determining the maximum height and time taken to reach it, while discussing the domain and range in context.

What is the maximum height the hot air balloon reaches during its flight?

• 400 feet

• 500 feet

• 450 feet

• 550 feet

How many seconds does it take for the balloon to reach its maximum height?

• 15 seconds

• 10 seconds

• 20 seconds

• 5 seconds

What is the absolute value of -5?

• 10

• 0

• 5

• -5

Which of the following is a common misunderstanding about absolute value?

• Absolute value is the distance from zero.

• Absolute value makes a number positive.

• Absolute value is the principal square root of a number squared.

• Absolute value is always negative.

What shape does the graph of an absolute value function form?

• A V shape

• A circle

• A parabola

• A straight line

What is the vertex of the graph of y = |x|?

• (0, 1)

• (1, 1)

• (0, 0)

• (-1, -1)

What effect does multiplying the absolute value function by a negative number have?

• It reflects the graph over the x-axis.

• It compresses the graph horizontally.

• It stretches the graph vertically.

• It shifts the graph to the right.

What is the horizontal shift of the function g(x) = -2|x + 1|?

• 1 unit to the right

• 1 unit to the left

• 2 units to the right

• 2 units to the left

In the context of the hot air balloon problem, what is the domain of the function?

• Negative infinity to positive infinity

• All real numbers

• 0 to 20

• 0 to 500

What is the range of the hot air balloon's height function?

• 0 to 500

• 0 to 20

• Negative infinity to positive infinity

• All real numbers