Understanding Transformations of Functions

The video tutorial explains the transformations of the basic function F(X) through vertical and horizontal stretches and compressions. It covers how multiplying the function values by a constant affects the graph vertically, and how multiplying the input values by a constant affects the graph horizontally. Examples are provided to illustrate vertical transformations with constants greater than 1 and between 0 and 1, as well as horizontal transformations with similar constants. The tutorial concludes with a summary of how these transformations alter the graph's appearance.

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

• It shifts to the right.

• It shifts to the left.

• It vertically stretches.

• It vertically compresses.

If the function F(X) is multiplied by 1/4, what transformation occurs?

• Horizontal compression by a factor of 1/4

• Vertical stretch by a factor of 4

• Vertical compression by a factor of 1/4

• Horizontal stretch by a factor of 4

How does multiplying the input of F(X) by a constant greater than 1 affect the graph?

• It vertically stretches the graph.

• It vertically compresses the graph.

• It horizontally compresses the graph.

• It horizontally stretches the graph.

What is the effect of multiplying the input of F(X) by 1/5?

• Vertical stretch by a factor of 5

• Horizontal compression by a factor of 5

• Horizontal stretch by a factor of 5

• Vertical compression by a factor of 5

When B is between 0 and 1, such as B = 1/2, what happens to the graph of F(X)?

• It shifts downwards.

• It becomes narrower.

• It shifts upwards.

• It becomes wider.

What transformation occurs when F(X) is replaced by F(2X)?

• Vertical stretch by a factor of 2

• Horizontal stretch by a factor of 2

• Vertical compression by a factor of 2

• Horizontal compression by a factor of 2

If F(X) is transformed to F(0.5X), what is the effect on the graph?

• Horizontal stretch by a factor of 2

• Horizontal compression by a factor of 2

• Vertical stretch by a factor of 2

• Vertical compression by a factor of 2

What is the result of multiplying each X coordinate by 1/B in a function transformation?

• Horizontal compression

• Vertical stretch

• Vertical compression

• Horizontal stretch

How does the graph of F(X) change when transformed to F(5X)?

• It becomes 1/5 as wide.

• It becomes 5 times wider.

• It shifts 5 units to the left.

• It shifts 5 units to the right.

What is the effect of the transformation Y = F(1/5X) on the graph of F(X)?

• It becomes 5 times narrower.

• It shifts downwards by 5 units.

• It becomes 5 times wider.

• It shifts upwards by 5 units.