Solving Absolute Value Equations and Inequalities by Graphing

This video tutorial covers solving absolute value equations and inequalities by graphing. It explains how to split equations into functions, interpret intersections, and use technology for graphing. The video also discusses solving inequalities by identifying intervals where one function is less than another and graphing single functions to find solutions.

What is the main topic of the final video in the chapter?

• Solving linear equations

• Solving exponential equations

• Solving quadratic equations

• Solving absolute value equations and inequalities

When solving absolute value equations by graphing, what is the significance of the intersections?

• They represent the average values

• They represent the solutions to the equation

• They represent the minimum values

• They represent the maximum values

In the example given, what are the x-values that produce a y-value of 42?

• 9 and -3

• 0 and 42

• 3 and 9

• 3 and -9

What is the first step in solving an absolute value inequality by graphing?

• Identifying the intervals where one function is less than the other

• Finding the minimum value

• Calculating the average value

• Finding the maximum value

In the inequality example, what is the interval of x-values that make the function less than 42?

• From -9 to 3, excluding -9 and 3

• From -12 to 16, excluding -12 and 16

• From -9 to 3, including -9 and 3

• From -12 to 16, including -12 and 16

How can the interval of x-values be expressed?

• As a maximum value

• As interval notation or inequality notation

• As a range of y-values

• As a single point

In the final example, what is the x-value that makes the blue function equal to zero?

• -1.5

• 1.5

• 3

• 0

Why is the x-axis used as a reference for zero in the final example?

• Because it represents the average value

• Because the y-value is zero along the x-axis

• Because it represents the minimum value

• Because it represents the maximum value

What tool is used to graph the functions in the examples?

• A calculator

• A ruler

• A protractor

• The Inspire graphing tool

What is the purpose of finding the intersection points in the graph?

• To determine the average values

• To determine the minimum values

• To determine the maximum values

• To determine the solutions to the equation or inequality