Transformations of Functions and Graphs

The video tutorial explains how to transform the graph of a function f(x) to obtain g(x) by applying vertical stretches, compressions, and shifts. It covers two examples: one involving a vertical stretch and downward shift, and another involving a vertical compression and upward shift. The process involves adjusting the y-coordinates of the endpoints of f(x) to graph g(x).

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

• It stretches vertically.

• It shifts vertically.

• It compresses vertically.

• It shifts horizontally.

In the transformation g(x) = 3f(x) - 2, what does the '-2' indicate?

• A horizontal shift left.

• A vertical shift down.

• A vertical stretch.

• A horizontal shift right.

How do you perform a vertical stretch by a factor of 3 on a point (x, y)?

• Multiply x by 3.

• Multiply y by 3.

• Add 3 to y.

• Subtract 3 from x.

What is the new y-coordinate of the point (4, 2) after applying the transformation g(x) = 3f(x) - 2?

• 10

• 8

• 6

• 4

What type of transformation is applied when f(x) is multiplied by 1/2?

• Vertical stretch

• Vertical compression

• Horizontal compression

• Horizontal stretch

In the transformation g(x) = 1/2f(x) + 4, what does the '+4' indicate?

• A vertical shift up.

• A vertical shift down.

• A horizontal shift left.

• A horizontal shift right.

How do you perform a vertical compression by a factor of 1/2 on a point (x, y)?

• Multiply x by 1/2.

• Subtract 1/2 from x.

• Add 1/2 to y.

• Multiply y by 1/2.

What is the new y-coordinate of the point (5, -6) after applying the transformation g(x) = 1/2f(x) + 4?

• 1

• 2

• 3

• 4

Which of the following transformations results in a graph being shifted upwards?

• Multiplying f(x) by a constant less than 1

• Adding a constant to f(x)

• Multiplying f(x) by a constant greater than 1

• Subtracting a constant from f(x)

What is the effect of adding a constant to the function f(x)?

• It results in a vertical stretch.

• It results in a vertical shift.

• It results in a horizontal shift.

• It results in a horizontal compression.