Characteristics of Absolute Value Functions

This video tutorial introduces the concept of absolute value, explaining its basic properties and formal definition. It explores how absolute value is applied in equations and inequalities, emphasizing its role as a measure of distance from a center. The tutorial also covers graphing the absolute value function, highlighting its V shape and key characteristics such as domain, range, and intercepts. Additionally, it demonstrates using Desmos to visualize and analyze absolute value functions.

What is the absolute value of -7?

• -7

• 7

• 14

• 0

According to the formal definition, what is the absolute value of x if x is less than zero?

• 0

• -x

• x^2

• x

If the absolute value of x equals 4, what are the possible values of x?

• 4 and 8

• -4 and 0

• 4 and 0

• 4 and -4

How far are you from the grocery store if it is located at -5 miles and you are at 0 miles?

• 0 miles

• 10 miles

• 5 miles

• -5 miles

What does the graph of the absolute value function look like?

• A straight line

• A parabola

• A V shape

• A circle

What is the domain of the absolute value function y = |x|?

• x ≥ 0

• x ≤ 0

• x ≠ 0

• All real numbers

Where does the absolute value function y = |x| touch the x-axis?

• At x = 0

• At x = 2

• At x = -1

• At x = 1

What is the range of the absolute value function y = |x|?

• y ≠ 0

• All real numbers

• y ≥ 0

• y ≤ 0

What happens to the graph of y = |x| when x is negative?

• It bends downwards

• It bends upwards

• It becomes a straight line

• It stays the same

Which tool can be used to explore the characteristics of the absolute value function?

• Python

• Google Sheets

• Desmos

• Excel