Exploring Reflections in Function Transformations

This video tutorial covers function transformations, focusing on reflections across the X and Y axes. It explains how changing the signs of 'A' and 'B' in function equations affects graph reflections. The tutorial uses T tables for comparison and provides visual animations to illustrate these transformations. Examples include square root and cubed root functions, demonstrating how to graph these transformations. The video concludes with a preview of upcoming topics on combined transformations.

What does changing the sign of 'A' in a function do to its graph?

• Reflects it across the y-axis

• Compresses it horizontally

• Reflects it across the x-axis

• Stretches it vertically

If y = f(-x), what transformation occurs to the graph of f(x)?

• Reflection across the x-axis

• Vertical stretch

• Reflection across the y-axis

• Horizontal compression

What is the result of reflecting the function f(x) = √x across the x-axis?

• h(x) = -√(-x)

• h(x) = √(-x)

• g(x) = √x

• g(x) = -√x

What happens to the graph of f(x) when the sign of the y-coordinates is changed?

• It compresses horizontally

• It stretches vertically

• It reflects across the x-axis

• It reflects across the y-axis

In the animation, what transformation is observed when 'A' changes from +1 to -1?

• Reflection across the y-axis

• Reflection across the x-axis

• Vertical compression

• Horizontal stretch

What transformation occurs when 'B' changes from 1 to -1?

• Reflection across the y-axis

• Reflection across the x-axis

• Horizontal compression

• Vertical stretch

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

• A U that opens downward

• A U that opens upward

• A V that opens upward

• A V that opens downward

What is the transformation of f(x) = -|x| compared to g(x) = |x|?

• Reflection across the x-axis

• Horizontal compression

• Reflection across the y-axis

• Vertical stretch

What is the result of graphing f(x) = ³√(-x)?

• Vertical stretch

• Horizontal compression

• Reflection across the x-axis

• Reflection across the y-axis

What is the transformation of the point (8, 2) when reflecting the function ³√x across the y-axis?

• (8, -2)

• (-8, -2)

• (-8, 2)

• (8, 2)