Graph Transformations and Reflections

The video tutorial explains how to transform the graph of f(x) = 2^x through vertical and horizontal shifts, as well as reflections across the x-axis and y-axis. It covers the mathematical principles behind these transformations and demonstrates them using a graphing calculator. The tutorial provides a comprehensive understanding of how to manipulate graphs using algebraic expressions.

What is the effect of adding a positive constant to a function f(x)?

• Shifts the graph to the right

• Shifts the graph downwards

• Shifts the graph to the left

• Shifts the graph upwards

If f(x) is shifted down by 2 units, which of the following represents the new function?

• f(x) - 2

• f(x - 2)

• f(x) + 2

• f(x + 2)

What happens to the graph of f(x) when you replace x with x - 4?

• The graph shifts 4 units down

• The graph shifts 4 units up

• The graph shifts 4 units to the right

• The graph shifts 4 units to the left

Which transformation reflects a function across the X-axis?

• f(x - 2)

• f(x) + 2

• -f(x)

• f(-x)

How do you reflect a function across the Y-axis?

• Add a constant to f(x)

• Replace x with -x

• Subtract a constant from f(x)

• Replace f(x) with -f(x)

What is the result of reflecting the graph of f(x) = 2^x across the X-axis?

• 2^-x

• 2^x

• -2^x

• -2^-x

Which of the following represents a reflection of f(x) = 2^x across the Y-axis?

• 2^-x

• -2^-x

• -2^x

• 2^x

What is the purpose of using a graphing calculator in this context?

• To solve algebraic equations

• To verify graph transformations

• To calculate derivatives

• To find integrals

How can you ensure the graphing calculator displays the standard window?

• Press ZOOM 6

• Press ZOOM 0

• Press ZOOM 9

• Press ZOOM 1

What does the graphing calculator show when you enter -2^x?

• A reflection across the Y-axis

• A shift to the left

• A reflection across the X-axis

• A shift to the right