Graph Transformations and Shifts

The video tutorial discusses transformations in function notation, focusing on how to transform graphs of functions. It provides examples of shifting and stretching graphs, identifies necessary transformations, and explores alternative methods to achieve the same graph. The tutorial suggests performing reflections and stretches before translations for efficiency.

What is the primary focus when discussing transformations in function notation?

• Altering the function's range

• Maintaining the same language in answers

• Simplifying the function's expression

• Changing the function's domain

When shifting a graph to the right by two units, which transformation is applied?

• Replace Y with Y + 2

• Replace X with X + 2

• Replace Y with Y - 2

• Replace X with X - 2

How do you perform a vertical translation downward by two units?

• Replace Y with Y + 2

• Replace Y with Y - 2

• Replace X with X - 2

• Replace X with X + 2

What is the effect of stretching a graph vertically by a factor of three?

• Replace X with X * 3

• Replace Y with Y / 3

• Replace X with X / 3

• Replace Y with Y * 3

What is the first step in identifying transformations to obtain a specific graph?

• Perform a vertical stretch

• Perform a horizontal shift

• Identify the desired final graph

• Identify the original graph

If a vertical shift does not achieve the desired transformation, what should be tried next?

• Reflection

• Horizontal shift

• Horizontal stretch

• Vertical stretch

How can you achieve a graph of y = f(x - 3)?

• Shift the graph 3 units downward

• Shift the graph 3 units upward

• Shift the graph 3 units to the right

• Shift the graph 3 units to the left

What is the suggested order of transformations for simplicity?

• Translations first, then reflections and stretches

• Only translations

• Only reflections

• Reflections and stretches first, then translations

What happens when you reflect a graph across the x-axis?

• The graph is inverted horizontally

• The graph is shifted downward

• The graph is inverted vertically

• The graph is shifted upward

What is the result of reflecting a graph across the y-axis?

• The graph is shifted to the right

• The graph is inverted vertically

• The graph is inverted horizontally

• The graph is shifted to the left