Graph Shifts and Function Analysis

The video tutorial explains how the graph of a cubic function, f(x) = x^3 - 3x^2 + 2x + 1, is transformed when a constant is added to the function, resulting in a vertical shift. The instructor demonstrates this by comparing the original graph with the transformed graph, f(x) + 3, and verifies the shift by checking specific points on the graph.

What is the original function given in the problem?

• f(x) = x^3 - 3x^2 + 2x + 1

• f(x) = x^2 - 3x + 2

• f(x) = x^3 + 3x^2 - 2x - 1

• f(x) = x^3 - 2x^2 + 3x + 1

What effect does adding a constant to a function have on its graph?

• It reflects the graph over the x-axis.

• It changes the shape of the graph.

• It shifts the graph vertically.

• It shifts the graph horizontally.

If a point on the original graph is at (0, 1), where will it be after shifting the graph up by 3?

• (0, 3)

• (0, 1)

• (0, -2)

• (0, 4)

Which line represents the graph of f(x) + 3?

• The blue line

• The green line

• The red line

• The yellow line

What is the new y-coordinate of the point (2, 1) after the graph is shifted up by 3?

• 4

• 1

• 5

• 2

What is the correct answer choice for the shifted graph?

• A

• C

• D

• B