Understanding Transformations of Functions

The video tutorial explains how to transform a function G(x) from F(x) by reflecting it across the X-axis and stretching it horizontally by a factor of 2. It covers the mathematical representation of these transformations, focusing on the values of 'A' and 'B' in the function G(x) = A * F(Bx). The tutorial also includes a review of reflections and horizontal stretches, providing examples and animations to verify the transformations.

What transformation is applied to F(x) to obtain G(x) in the given problem?

• Horizontal stretch and vertical compression

• Vertical stretch and horizontal compression

• Reflection across the x-axis and horizontal stretch

• Reflection across the y-axis and vertical stretch

Which parameter affects the reflection across the x-axis?

• Parameter B

• Parameter A

• Parameter D

• Parameter C

What is the value of A for the reflection across the x-axis?

• 1

• 2

• 0

• -1

How is the horizontal stretch by a factor of 2 represented in the function?

• B = -1/2

• B = -2

• B = 1/2

• B = 2

What is the reciprocal of the horizontal stretch factor in this problem?

• 1/2

• 1

• 2

• 1/4

What is the purpose of changing the sign of F(x) in the transformation?

• To stretch the graph vertically

• To shift the graph upwards

• To reflect the graph across the x-axis

• To compress the graph horizontally

What happens to the graph of F(x) when A is set to -1?

• It reflects across the y-axis

• It reflects across the x-axis

• It shifts upwards

• It compresses horizontally

What is the effect of setting B to 1/2 on the graph?

• It compresses vertically

• It stretches vertically

• It stretches horizontally

• It compresses horizontally

What is the final form of the function G(x) after applying the transformations?

• G(x) = -F(1/2x)

• G(x) = F(2x)

• G(x) = F(-1/2x)

• G(x) = -F(2x)

Which transformation is NOT part of the problem discussed?

• Reflection across the x-axis

• Horizontal compression

• Horizontal stretch

• Vertical stretch