Understanding Transformations of Absolute Value Functions

The video tutorial explains how to determine the equation of a transformed graph based on the absolute value function. It covers the reflection and compression of the graph, as well as horizontal and vertical shifts. The tutorial guides viewers through calculating transformation parameters and solving for the value of 'A' using a specific point on the graph. The process is concluded with a practical example.

What is the basic function used as a reference for the transformation?

• Y = X^2

• Y = X^3

• Y = 1/X

• Y = |X|

Which transformation reflects the graph across the x-axis?

• Vertical compression

• Reflection

• Vertical stretch

• Horizontal shift

If a graph is shifted right by 1 unit, what is the value of C?

• -1

• -2

• 1

• 2

What does a negative value of D indicate about the graph's shift?

• Shifted right

• Shifted up

• Shifted left

• Shifted down

How is the function G(X) expressed in terms of F(X) after considering shifts?

• G(X) = A * F(X - C) - D

• G(X) = A * F(X + C) + D

• G(X) = A * F(X - C) + D

• G(X) = A * F(X + C) - D

What is the value of A if the graph is vertically compressed by a factor of 1/2?

• 1

• -1

• 1/2

• -1/2

Which point on the red graph is used to solve for A?

• (2, 1)

• (0, 0)

• (-3, -4)

• (1, -2)

What does the negative sign of A indicate about the graph?

• Vertical stretch

• No transformation

• Horizontal shift

• Reflection

What is the final equation for G(X) after all transformations?

• G(X) = -1/2 * |X - 1| + 2

• G(X) = -1/2 * |X + 1| + 2

• G(X) = -1/2 * |X - 1| - 2

• G(X) = 1/2 * |X - 1| - 2

What is the effect of a vertical compression on the graph's shape?

• Makes it narrower

• Reflects it

• Makes it wider

• Shifts it