Exploring Absolute Value Transformations

The video tutorial covers absolute value functions, focusing on the parent function f(x) = |x| and how transformations affect it. The H value shifts the vertex horizontally, while the K value moves it vertically. The A value influences vertical stretch or compression and reflection across the x-axis. The tutorial includes examples and graphing exercises to illustrate these concepts.

What is the parent function of an absolute value function?

• f(x) = x - 1

• f(x) = x + 1

• f(x) = |x|

• f(x) = x^2

How does the H value affect the vertex of the function f(x) = |x - H|?

• Moves the vertex up and down

• Moves the vertex left and right

• Reflects the graph across the x-axis

• Changes the slope

If the function is f(x) = |x + 3|, in which direction does the vertex move?

• 3 units up

• 3 units to the right

• 3 units to the left

• 3 units down

What does the K value do in the function f(x) = |x| + K?

• Moves the vertex left and right

• Changes the slope

• Moves the vertex up and down

• Reflects the graph across the x-axis

In the function f(x) = |x| - 4, where does the vertex move?

• 4 units up

• 4 units down

• 4 units to the right

• 4 units to the left

What does a vertical stretch mean in the context of the A value?

• The graph becomes wider

• The graph moves down

• The graph moves up

• The graph becomes narrower

If A is less than 1, what happens to the graph of the function?

• It becomes wider

• It moves up

• It moves down

• It becomes narrower

What effect does a negative A value have on the graph?

• Reflects it across the x-axis

• Moves it down

• Moves it up

• Reflects it across the y-axis

In the function f(x) = -2|x|, what happens to the graph?

• It is reflected across the y-axis and becomes wider

• It is reflected across the x-axis and becomes narrower

• It moves up and becomes narrower

• It moves down and becomes wider

If the function is f(x) = 3|x + 1| - 2, what is the combined effect on the graph?

• Moves left 1, up 2, and becomes narrower

• Moves left 1, down 2, and becomes narrower

• Moves right 1, down 2, and becomes wider

• Moves right 1, up 2, and becomes wider