Transformations between functions

The video tutorial explains how to perform transformations on functions to achieve desired forms. It covers transforming F of X to G of X, H of X to match G of X, and K of X to achieve specific transformations. Key concepts include vertical stretches, horizontal shifts, reflections, and compressions. The tutorial aims to demystify transformations and make learners comfortable with applying them to different functions.

What is the initial transformation needed to obtain G(x) from F(x)?

• Vertical stretch by a factor of 2

• Vertical stretch by a factor of 3

• Horizontal shift to the right by 2 units

• Horizontal shift to the left by 2 units

How should the graph of F(x) be shifted to align with G(x)?

• Shift 1 unit down

• Shift 2 units to the left

• Shift 1 unit up

• Shift 2 units to the right

What transformation is applied to H(x) to achieve a vertical stretch of 2?

• Multiply by 4

• Multiply by 2

• Multiply by 1/4

• Multiply by 1/2

Which transformation is necessary to remove the reflection about the Y-axis in H(x)?

• Shift 1 unit down

• Reflect about the Y-axis

• Shift 1 unit up

• Reflect about the X-axis

What is the final vertical transformation needed for K(x)?

• Vertical compression by a factor of 1/4

• Vertical stretch by a factor of 3

• Vertical stretch by a factor of 2

• Vertical compression by a factor of 1/2

How is the horizontal stretch of 1/2 in K(x) adjusted?

• Horizontal stretch by a factor of 1/2

• Horizontal compression by a factor of 2

• Horizontal compression by a factor of 1/4

• Horizontal stretch by a factor of 2

What is the final horizontal transformation applied to K(x)?

• Shift 1 unit to the left

• Shift 2 units to the right

• Shift 1 unit to the right

• Shift 2 units to the left