Understanding Function Transformations

The video tutorial explains how to describe a function G(x) in terms of F(x) by applying transformations. It covers vertical stretching by a factor of 3, shifting left by 2 units, and shifting down by 4 units. The tutorial provides a formula for G(x) and explains the roles of parameters A, C, and D in these transformations. An example using the square root function is provided to verify the transformations, demonstrating the expected changes in the graph.

What transformation is applied to F(x) to obtain G(x) if G(x) is vertically stretched by a factor of 3?

• G(x) = 3 * F(x)

• G(x) = F(x) / 3

• G(x) = F(x) + 3

• G(x) = F(x) - 3

In the transformation formula G(x) = A * F(x + C) + D, what does the value of C represent?

• Compression factor

• Vertical stretch factor

• Vertical shift

• Horizontal shift

If a graph is vertically stretched by a factor of 3, what is the value of A?

• 1

• 3

• 0

• -3

What happens to the graph of F(x) if C is positive in the transformation G(x) = A * F(x + C) + D?

• The graph shifts down

• The graph shifts right

• The graph shifts up

• The graph shifts left

If the graph is shifted left by 2 units, what is the value of C?

• -4

• 0

• 2

• -2

What is the effect of a negative D value in the transformation G(x) = A * F(x + C) + D?

• The graph compresses horizontally

• The graph stretches vertically

• The graph shifts down

• The graph shifts up

In the example, what is the final form of G(x) after applying all transformations?

• G(x) = 3 * F(x - 2) + 4

• G(x) = 3 * F(x + 2) - 4

• G(x) = F(x + 2) - 4

• G(x) = 3 * F(x) + 2

How does changing A to 3 affect the basic square root function?

• It shifts the graph horizontally

• It shifts the graph vertically

• It compresses the graph vertically

• It stretches the graph vertically

What is the result of changing C to +2 in the square root function example?

• The graph moves up two units

• The graph moves down two units

• The graph moves left two units

• The graph moves right two units

What is the effect of setting D to -4 in the square root function example?

• The graph moves up four units

• The graph compresses vertically

• The graph moves down four units

• The graph stretches horizontally