Understanding Function Shifts

The video tutorial explains how to graph the function G(x) = (x - 2)^2 + 4 by shifting the graph of f(x) = x^2. It covers the process of making G(x) overlap with f(x) and highlights the differences between the two functions. The tutorial details how to shift the graph of G(x) two units to the right and four units down, providing a clear understanding of graph transformations.

What is the original function f(x) given in the video?

• f(x) = x^3

• f(x) = x + 2

• f(x) = x^2

• f(x) = x - 2

What is the expression for g(x) that needs to be graphed?

• g(x) = (x + 2)^2 - 4

• g(x) = (x - 2)^2 + 4

• g(x) = (x - 2)^2 - 4

• g(x) = (x + 2)^2 + 4

What is the first step to make g(x) overlap with f(x)?

• Shift g(x) up

• Shift g(x) down

• Shift g(x) to the left

• Shift g(x) to the right

How does the expression (x - 2)^2 affect the graph of g(x)?

• It shifts the graph down

• It shifts the graph to the right

• It shifts the graph to the left

• It shifts the graph up

Why is the shift to the right counterintuitive?

• Because it involves division

• Because of the positive sign

• Because of the negative sign

• Because it involves multiplication

What does the constant term +4 do to the graph of g(x)?

• Shifts it down

• Shifts it up

• Shifts it left

• Shifts it right

How many units is the graph of g(x) shifted vertically?

• 5 units

• 4 units

• 3 units

• 2 units

What is the new coordinate of the point (2, 0) after shifting?

• (2, -4)

• (2, 4)

• (0, -4)

• (4, 0)

What is the overall transformation applied to f(x) to get g(x)?

• Shifted right and up

• Shifted left and down

• Shifted right and down

• Shifted left and up

What is the new vertex of the graph after transformation?

• (4, 0)

• (2, 4)

• (2, -4)

• (0, 0)