Understanding Graph Transformations

The video tutorial explains graph transformations using f(x) = x^2 and g(x) = f(x + 3) - 2. It covers vertical and horizontal shifts, demonstrating how to graph g(x) by shifting f(x) down two units and left three units. A second example shows g(x) = f(x - 2) + 4, with shifts up four units and right two units. The tutorial uses animations and key points to illustrate these transformations.

What is the initial function given in the first example?

• f(x) = x - 2

• f(x) = x + 3

• f(x) = x^2

• f(x) = x^3

In a vertical shift, if d is positive, how does the graph of g(x) = f(x) + d move?

• Left d units

• Up d units

• Down d units

• Right d units

What happens to the graph of g(x) = f(x) - d when d is negative?

• It shifts right d units

• It shifts left d units

• It shifts down d units

• It shifts up d units

In a horizontal shift, if c is positive, how does the graph of g(x) = f(x + c) move?

• Up c units

• Down c units

• Left c units

• Right c units

What is the effect on the graph of g(x) = f(x - c) when c is negative?

• It shifts left c units

• It shifts right c units

• It shifts down c units

• It shifts up c units

How is the graph of g(x) = f(x+3) - 2 transformed from f(x) = x^2?

• Shifted up 3 units and right 2 units

• Shifted down 2 units and left 3 units

• Shifted up 2 units and left 3 units

• Shifted down 3 units and right 2 units

What are the coordinates of the vertex after transforming f(x) = x^2 to g(x) = f(x+3) - 2?

• (3, 2)

• (-3, -2)

• (0, 0)

• (-2, -3)

In the second example, what is the transformation applied to g(x) = f(x-2) + 4?

• Shifted down 2 units and left 4 units

• Shifted up 4 units and right 2 units

• Shifted down 4 units and right 2 units

• Shifted up 4 units and left 2 units

What is the value of d in the transformation g(x) = f(x-2) + 4?

• 2

• -2

• 4

• -4

How does the graph of g(x) = f(x-2) + 4 compare to f(x) = x^2?

• It is shifted up 4 units and left 2 units

• It is shifted down 2 units and left 4 units

• It is shifted down 4 units and right 2 units

• It is shifted up 4 units and right 2 units