Understanding Graph Transformations

The video tutorial explains how to determine the equation of a transformed graph based on the absolute value function. It covers identifying transformations such as vertical stretch and shifts, calculating transformation values, and verifying these calculations. The tutorial provides methods to determine the values of A, C, and D, and concludes with a verification process to ensure accuracy.

What is the basic function used as a reference for determining the red graph's equation?

• Exponential function

• Quadratic function

• Linear function

• Absolute value function

What type of transformation is assumed for the red graph initially?

• Translation

• Reflection

• Vertical stretch

• Horizontal stretch

How is the red graph shifted compared to the black graph?

• Down 3 units and right 2 units

• Down 2 units and left 3 units

• Up 2 units and right 3 units

• Up 3 units and left 2 units

What is the value of A if the red graph is vertically stretched?

• 1

• 4

• 2

• 3

What is the value of C if the graph is shifted left?

• 2

• -3

• 0

• 3

What is the value of D if the graph is shifted down?

• 0

• 2

• -2

• -3

What is the final equation for G(x) after determining A, C, and D?

• G(x) = 2|x - 3| + 2

• G(x) = 2|x + 3| - 2

• G(x) = 2|x + 3| + 2

• G(x) = |x + 3| - 2

What alternative method can be used to determine the value of A?

• Guessing the value

• Using a graphing calculator

• Using a different function

• Selecting a point on the red graph

Which point on the red graph is used in the alternative method to find A?

• (-3, -2)

• (-4, 0)

• (0, 0)

• (3, 2)

What is the result of solving for A using the point (-4, 0)?

• A = 3

• A = 2

• A = 1

• A = 4