Graph Transformations and Reflections

The video tutorial explains graphing techniques using transformations of functions, focusing on the absolute value function. It covers vertical shifts, reverse horizontal shifts, and reflections about the x-axis, y-axis, and origin. Examples demonstrate how these transformations affect the graph, emphasizing the importance of checking results with a graphing calculator.

What is the primary function used in the video to demonstrate transformations?

• Logarithmic function

• Exponential function

• Absolute value function

• Quadratic function

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

• The graph moves up

• The graph shifts to the right

• The graph shifts to the left

• The graph moves down

In a reverse horizontal shift, what direction does the graph move when a positive constant is added inside the function?

• To the left

• Downwards

• To the right

• Upwards

Which transformation is described as the 'reverse' of what is expected?

• Vertical shift

• Horizontal shift

• Reflection

• Rotation

Which transformation involves using the x-axis as a mirror?

• Reflection

• Rotation

• Horizontal shift

• Vertical shift

What is the result of applying a negative sign outside the function f(x)?

• The graph reflects over the y-axis

• The graph shifts to the right

• The graph shifts to the left

• The graph reflects over the x-axis

Which transformation uses the y-axis as a mirror?

• Reflection over the y-axis

• Horizontal shift

• Vertical shift

• Reflection over the x-axis

What is the effect of subtracting a constant outside the absolute value function?

• The graph shifts to the right

• The graph moves down

• The graph moves up

• The graph shifts to the left

If f(x) = |x| is transformed to f(x) = |x| - 2, what is the transformation?

• Horizontal shift right by 2

• Horizontal shift left by 2

• Vertical shift down by 2

• Vertical shift up by 2

In the example of f(x) = |x - 3|, what type of shift occurs?

• Vertical shift

• Reflection

• Horizontal shift to the right

• Horizontal shift to the left