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 begins by identifying the basic shape of the absolute value graph and then discusses how to recognize transformations such as shifts. The tutorial focuses on calculating the values of C and D, which represent horizontal and vertical shifts, respectively. Finally, it demonstrates how to write the equation for the transformed graph, ensuring a clear understanding of the transformation process.

What is the basic function used as a reference for determining the transformed graph?

• Y = |X|

• Y = X^2

• Y = X^3

• Y = 1/X

How can we tell that the graph has not been vertically or horizontally stretched?

• The graph is a straight line.

• The slopes on both sides remain unchanged.

• The graph is a circle.

• The graph is a parabola.

What indicates that the graph has been shifted right and up?

• The graph's low point is at the origin.

• The graph's low point is at (2,1).

• The graph is a horizontal line.

• The graph is a vertical line.

What is the significance of the point (2,1) in the context of the graph transformation?

• It is the midpoint of the graph.

• It is the point of intersection with the x-axis.

• It is the new low point of the graph.

• It is the point of intersection with the y-axis.

What is the role of the values A, B, C, and D in the transformation function?

• They determine the color of the graph.

• They transform the basic function F(x).

• They determine the size of the graph.

• They transform the graph into a circle.

What is the effect of a negative C value in the transformation function?

• The graph shifts left.

• The graph shifts right.

• The graph shifts up.

• The graph shifts down.

What is the value of D if the graph is shifted up by one unit?

• D = -1

• D = 0

• D = 1

• D = 2

What happens to the graph when D is negative?

• The graph shifts left.

• The graph shifts right.

• The graph shifts up.

• The graph shifts down.

How is the transformation function G(x) expressed in terms of F(x)?

• G(x) = F(x) + 2

• G(x) = F(x) - 1

• G(x) = F(x - 2) + 1

• G(x) = F(x + 2) - 1

What is the equivalent expression for G(x) in terms of Y?

• Y = |X + 2| - 1

• Y = |X| + 2

• Y = |X - 2| + 1

• Y = |X| - 1