Understanding Horizontal Stretch and Compression

The video tutorial explains how to identify horizontal stretches and compressions in function transformations. It introduces the concept of transformations using the equation G(X) = A x F(BX) and focuses on determining the values of A and B. The tutorial uses coordinate analysis to demonstrate how to identify these transformations, emphasizing that changes in X coordinates indicate horizontal transformations. It provides examples to illustrate the process of solving for B, including the use of reciprocals and equations. The video also covers reflections across the Y-axis when B is negative.

What is the purpose of analyzing the coordinates of corresponding points in the context of horizontal transformations?

• To calculate the area under the curve

• To find the slope of the line

• To determine the color of the graph

• To identify the values of A and B

In the first example, what indicates that there is no vertical stretch or compression?

• The Y coordinates are the same

• The X coordinates are the same

• The function is quadratic

• The graph is a straight line

What is the value of A in the first example, and why?

• A = 3, because the graph is shifted

• A = 2, because there is a vertical stretch

• A = 0.5, because there is a vertical compression

• A = 1, because there is no vertical stretch or compression

How is a horizontal stretch identified in the transformation equation G(X) = A x F(BX)?

• When B is less than 1

• When A is less than 1

• When A is greater than 1

• When B is greater than 1

What happens to the graph when B is negative in the transformation equation?

• The graph is stretched vertically

• The graph is reflected across the Y-axis

• The graph is shifted upwards

• The graph is compressed vertically

In the second example, what transformation occurs along with horizontal compression?

• Reflection across the X-axis

• Vertical compression

• Vertical stretch

• Reflection across the Y-axis

How do you determine the value of B in a horizontal transformation?

• By finding the reciprocal of the multiplication factor

• By dividing the Y coordinates

• By adding the X coordinates

• By subtracting the Y coordinates

What is the value of B in the second example, and what does it signify?

• B = 3, indicating a vertical stretch

• B = -3, indicating a reflection and compression

• B = 0.5, indicating a horizontal stretch

• B = 2, indicating a vertical compression

What is the significance of the reciprocal in determining the value of B?

• It determines the color of the graph

• It is used to find the correct B value for horizontal transformations

• It helps in finding the slope

• It calculates the area under the curve

What is the final transformation equation for G(X) in the second example?

• G(X) = F(3X)

• G(X) = F(-0.5X)

• G(X) = F(-3X)

• G(X) = F(0.5X)