Transformations of Functions and Graphs

The video tutorial explains how to graphically transform functions using vertical stretches, compressions, and shifts. It provides two examples: the first demonstrates a vertical stretch by a factor of two, a right shift of three units, and an upward shift of one unit. The second example illustrates a vertical compression by a factor of one-half, a left shift of two units, and a downward shift of three units. The tutorial guides viewers through calculating new endpoints for the transformed graph and plotting them.

What does the '2' in g(x) = 2 * f(x - 3) + 1 represent?

• Horizontal compression by a factor of 2

• Vertical stretch by a factor of 2

• Vertical shift by 2 units

• Horizontal shift by 2 units

How does the transformation x - 3 affect the graph of f(x)?

• Compresses the graph horizontally

• Stretches the graph vertically

• Shifts the graph right by 3 units

• Shifts the graph left by 3 units

What is the new y-coordinate after applying a vertical stretch by a factor of 2 to the point (1, 3)?

• 3

• 6

• 2

• 1

After shifting the graph up by 1 unit, what is the new y-coordinate of the point (1, 6)?

• 8

• 6

• 5

• 7

What is the final transformed point of (1, 3) after all transformations?

• (1, 1)

• (2, 6)

• (3, 5)

• (4, 7)

In the second example, what does the '1/2' in g(x) = 1/2 * f(x + 2) - 3 represent?

• Horizontal compression by a factor of 1/2

• Horizontal stretch by a factor of 1/2

• Vertical compression by a factor of 1/2

• Vertical stretch by a factor of 1/2

How does the transformation x + 2 affect the graph of f(x)?

• Shifts the graph left by 2 units

• Shifts the graph right by 2 units

• Stretches the graph vertically

• Compresses the graph horizontally

What is the new y-coordinate after applying a vertical compression by a factor of 1/2 to the point (3, -4)?

• -3

• -2

• -4

• -1

After shifting the graph down by 3 units, what is the new y-coordinate of the point (1, 6)?

• 3

• 0

• 6

• 1

What is the final transformed point of (3, -4) after all transformations?

• (1, -1)

• (2, -3)

• (1, -5)

• (0, -2)