Understanding Transformations of Functions

The video tutorial explains transformations of the basic function F(X) through vertical and horizontal stretches and compressions. It covers how multiplying F(X) by a constant affects the Y-axis, resulting in vertical transformations, and how multiplying the input X by a constant affects the X-axis, leading to horizontal transformations. The tutorial provides examples with specific values to illustrate these concepts, such as Y = 4xF(X) for vertical stretch and Y = F(5X) for horizontal compression. The video concludes with practical examples using the function F(X) = X squared.

What type of transformation occurs when F(X) is multiplied by a constant greater than 1?

• Horizontal stretch

• Horizontal compression

• Vertical compression

• Vertical stretch

If Y = 1/4 x F(X), what transformation does F(X) undergo?

• Horizontal compression by 1/4

• Vertical compression by 1/4

• Vertical stretch by 4

• Horizontal stretch by 4

What happens to the graph of F(X) when the input is multiplied by a constant greater than 1?

• It is horizontally stretched

• It is vertically stretched

• It is vertically compressed

• It is horizontally compressed

For Y = F(5X), what transformation occurs to F(X)?

• Horizontal stretch by 5

• Vertical compression by 1/5

• Horizontal compression by 1/5

• Vertical stretch by 5

In the function Y = F(1/5X), what is the effect on the graph of F(X)?

• Vertical compression by 5

• Horizontal compression by 5

• Horizontal stretch by 5

• Vertical stretch by 5

What is the result of applying a horizontal stretch to F(X) when B is between 0 and 1?

• The graph becomes wider

• The graph shifts downwards

• The graph becomes narrower

• The graph shifts upwards

How does the graph of Y = 4X^2 compare to the graph of Y = X^2?

• It is horizontally compressed

• It is vertically stretched

• It is horizontally stretched

• It is vertically compressed

What transformation does Y = 1/25X^2 represent?

• Horizontal stretch by 25

• Vertical compression by 1/25

• Vertical stretch by 25

• Horizontal compression by 1/25

If F(X) = X^2, what is the transformed function for Y = F(5X)?

• Y = X^2/5

• Y = 5X^2

• Y = X^2/25

• Y = 25X^2

For the function Y = 1/4X^2, what transformation has been applied to F(X) = X^2?

• Vertical stretch by 4

• Horizontal compression by 1/4

• Vertical compression by 1/4

• Horizontal stretch by 4