Understanding Absolute Value Functions

The video tutorial covers the concept of absolute value, explaining its definition and conditions. It introduces piecemeal functions, demonstrating how they work with examples. The tutorial then focuses on graphing absolute value functions, highlighting the importance of understanding their structure. Finally, it shows how to use graphs to solve inequalities, emphasizing the visual interpretation of mathematical concepts.

What is the absolute value of x-3 when x is greater than 3?

• x - 3

• 3 + x

• x + 3

• 3 - x

What is a piecemeal function?

• A function that is always linear

• A function with no defined domain

• A function that changes based on the input value

• A function defined by a single equation

How does the graph of y = x look when x is less than or equal to zero?

• A circle

• A parabola

• A hyperbola

• A straight line

What is the significance of x=3 in the graph of y=|x-3|?

• It is the maximum point

• It is the y-intercept

• It is the minimum point

• It is the junction between two functions

What is the y-intercept of the graph when x is less than 3?

• 3

• -3

• 1

• 0

Why are absolute value graphs often referred to as 'bouncy' graphs?

• They are always increasing

• They have no intercepts

• They reflect off the x-axis

• They have a circular shape

What does the graph of y = |x-3| look like when x is less than 3?

• It is a horizontal line

• It is a vertical line

• It slopes upwards

• It slopes downwards

What happens to the graph of y=|x-3| when x is greater than or equal to 3?

• It curves downwards

• It continues as a straight line with a positive slope

• It becomes a vertical line

• It becomes a horizontal line

What is the solution set for the inequality |x-3| ≤ 4?

• x is between -1 and 7

• x is greater than 7

• x is less than -1

• x is between 0 and 4

How can you determine the solution to an inequality using a graph?

• By identifying the region below the line

• By calculating the slope

• By identifying the region above the line

• By finding the x-intercepts