Exploring Horizontal and Vertical Function Transformations

This video tutorial covers the transformation of functions, focusing on how adding constants to the domain or range affects the function's graph. It begins with an introduction to function transformations using the absolute value function as an example. The tutorial explains vertical shifts by adding a constant K to the function and horizontal shifts by adding a constant H to the variable X. It also compares different transformations by changing constants and encourages viewers to practice using online tools like Desmos.

What is the shape of the graph of the absolute value function?

• A circle

• A parabola

• A straight line

• A V-shape

What happens to the graph of a function when a positive constant is added to it?

• It shifts to the right

• It moves down

• It moves up

• It shifts to the left

What is the effect of subtracting a constant from a function?

• The graph moves up

• The graph shifts to the right

• The graph moves down

• The graph shifts to the left

When a constant is added directly to the variable inside the function, what is the effect on the graph?

• It shifts to the right

• It shifts to the left

• It moves up

• It moves down

What happens to the graph when a negative constant is added to the variable inside the function?

• It moves up

• It shifts to the right

• It moves down

• It shifts to the left

If the function is f(x) = |x + 3|, what happens to the graph if it is changed to f(x) = |x + 1|?

• It moves up

• It shifts to the right

• It moves down

• It shifts to the left

What is the effect of subtracting a constant from the variable inside the function?

• The graph moves down

• The graph shifts to the left

• The graph moves up

• The graph shifts to the right

If the function is f(x) = |x + 3| and it is changed to f(x) = |x + 3| - 2, what happens to the graph?

• It shifts to the left

• It moves up

• It moves down

• It shifts to the right

What is the effect of adding a constant to the end of a function?

• The graph moves down

• The graph shifts to the left

• The graph moves up

• The graph shifts to the right

Which online tool is recommended for exploring function transformations?

• GeoGebra

• Wolfram Alpha

• Desmos

• Khan Academy