Function Transformations and Reflections

This video tutorial covers function transformations, focusing on reflections across the x-axis and y-axis. It explains how changing the sign of 'A' and 'B' affects the graph of a function. The video uses T tables and graphing to demonstrate these transformations, and includes animations to visualize the changes. Examples are provided to illustrate the concepts, and the video concludes with a preview of upcoming topics on combined transformations.

What is the effect of changing the sign of 'A' in a function transformation?

• It results in a horizontal stretch.

• It reflects the function across the x-axis.

• It reflects the function across the y-axis.

• It results in a vertical stretch.

How does changing the sign of 'B' affect the graph of a function?

• It reflects the graph across the x-axis.

• It reflects the graph across the y-axis.

• It results in a horizontal compression.

• It results in a vertical compression.

What happens to the graph of f(x) = √x when it is transformed to g(x) = -√x?

• The graph is reflected across the y-axis.

• The graph is shifted downwards.

• The graph is reflected across the x-axis.

• The graph is shifted upwards.

In the context of function transformations, what does the expression h(x) = f(-x) represent?

• A vertical stretch.

• A horizontal compression.

• A reflection across the y-axis.

• A reflection across the x-axis.

What is the visual effect of changing 'A' from +1 to -1 in a function?

• A horizontal stretch followed by a reflection across the y-axis.

• A vertical compression followed by a reflection across the x-axis.

• A vertical stretch followed by a reflection across the y-axis.

• A horizontal compression followed by a reflection across the x-axis.

When 'B' changes from 1 to -1, what transformation occurs?

• A vertical stretch followed by a reflection across the x-axis.

• A horizontal stretch followed by a reflection across the y-axis.

• A vertical compression followed by a reflection across the y-axis.

• A horizontal compression followed by a reflection across the x-axis.

What is the parent function of f(x) = |x|?

• A V-shaped graph that opens downward.

• A U-shaped graph that opens upward.

• A V-shaped graph that opens upward.

• A U-shaped graph that opens downward.

How does the graph of f(x) = -|x| differ from its parent function?

• It shifts to the right.

• It opens upward instead of downward.

• It shifts to the left.

• It opens downward instead of upward.

What transformation occurs when graphing f(x) = ∛(-x)?

• A vertical stretch.

• A horizontal compression.

• A reflection across the y-axis.

• A reflection across the x-axis.

What is the next topic to be covered in the upcoming videos?

• Advanced calculus techniques.

• Combined function transformations.

• Graphing linear functions.

• Basic algebraic equations.