Transformations of Functions and Graphs

The video tutorial explains how to graphically transform functions using vertical stretches, compressions, and horizontal shifts. It provides a detailed explanation of how these transformations affect the graph of a function, using two examples to illustrate the concepts. The first example demonstrates a vertical stretch and a left shift, while the second example shows a vertical compression and a right shift. The tutorial emphasizes the importance of understanding how these transformations impact the coordinates of the graph's endpoints.

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

• A horizontal shift left by 2 units

• A vertical stretch by a factor of 2

• A horizontal shift right by 2 units

• A vertical compression by a factor of 2

If g(x) = a * f(x) and a > 1, what transformation occurs?

• Horizontal shift right

• Vertical stretch

• Vertical compression

• Horizontal shift left

How does the graph shift if g(x) = f(x - c) and c > 0?

• Left by c units

• Right by c units

• Down by c units

• Up by c units

To shift a graph left by 3 units, what operation is performed on the x-coordinates?

• Add 3

• Multiply by 3

• Subtract 3

• Divide by 3

What are the new coordinates of the endpoint (-2, -1) after a vertical stretch by 2 and a shift left by 3?

• (-5, -1)

• (-2, -3)

• (-5, -2)

• (-2, -2)

In the transformation g(x) = 1/3 * f(x - 2), what does the 1/3 represent?

• Horizontal shift left by 1/3 units

• Vertical stretch by a factor of 3

• Vertical compression by a factor of 1/3

• Horizontal shift right by 1/3 units

What is the effect of x - 2 in the function g(x) = 1/3 * f(x - 2)?

• Shift right by 2 units

• Shift down by 2 units

• Shift up by 2 units

• Shift left by 2 units

After applying a vertical compression by 1/3 and a shift right by 2 units, what are the new coordinates of the endpoint (-5, 3)?

• (-3, 1)

• (-3, 3)

• (-5, 1)

• (-5, 3)

What is the new y-coordinate of the endpoint (3, -6) after a vertical compression by 1/3?

• -2

• -6

• -1

• -3

What is the final position of the endpoint (3, -6) after applying the transformations in the second example?

• (5, -2)

• (3, -2)

• (3, -6)

• (5, -6)