Transformations of Absolute Value Functions

The video tutorial covers transformations of the absolute value function, focusing on graphing techniques, horizontal and vertical shifts, and understanding the role of slope and reflection. It explains how to determine the vertex, axis of symmetry, and how these transformations affect the domain and range of the function. The tutorial provides examples and encourages viewers to practice graphing without tables.

What is the main topic of the video?

• Transformations of the absolute value function

• Solving inequalities

• Transformations of the quadratic function

• Graphing linear equations

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

• A straight line

• A circle

• A parabola

• A V shape

What happens to the graph of the absolute value function when it is shifted vertically?

• It moves up or down

• It becomes narrower

• It becomes wider

• It moves left or right

How do you determine the new vertex when the absolute value function is shifted vertically?

• By adding or subtracting from the x-coordinate

• By adding or subtracting from the y-coordinate

• By multiplying the x-coordinate

• By dividing the y-coordinate

What is the effect of a horizontal shift on the absolute value function?

• It moves the graph up or down

• It changes the slope of the graph

• It reflects the graph

• It moves the graph left or right

How do you determine the direction of a horizontal shift?

• By the axis of symmetry

• By the sign of the number inside the absolute value

• By the slope of the graph

• By the sign of the number outside the absolute value

What is the axis of symmetry in a transformed absolute value function?

• The line x = 0

• The line x = h

• The line y = k

• The line y = 0

In the general form of the absolute value function, what does the 'a' value represent?

• The slope or reflection

• The vertical shift

• The horizontal shift

• The axis of symmetry

What happens to the graph when the 'a' value is negative?

• It reflects over the x-axis

• It shifts to the left

• It shifts to the right

• It reflects over the y-axis

How is the domain of a transformed absolute value function affected?

• It is limited to integers

• It remains all real numbers

• It is limited to negative numbers

• It is limited to positive numbers