Graph Transformations and Properties

The video tutorial explains transformations of the x cubed graph, focusing on movements and flips over the x-axis. It covers how to plot transformed points and provides an example of graph transformation using algebraic methods. The tutorial emphasizes understanding the effects of transformations on the graph's key points and intercepts.

What are the key points of the base graph of y = x^3?

• (0, 0), (1, 2), (2, 8), (-1, -2), (-2, -8)

• (0, 0), (1, 1), (2, 8), (-1, -1), (-2, -8)

• (0, 0), (1, 2), (2, 4), (-1, -2), (-2, -4)

• (0, 0), (1, 1), (2, 4), (-1, -1), (-2, -4)

What does a negative sign outside the function indicate in terms of graph transformation?

• A shift to the right

• A shift to the left

• A flip over the y-axis

• A flip over the x-axis

How does moving the graph two units to the right and one unit down affect the origin?

• The origin moves to (-2, 1)

• The origin remains unchanged

• The origin moves to (2, -1)

• The origin moves to (1, -2)

When plotting the transformed graph, what is the new position of the point (1, 1) after a flip over the x-axis?

• (1, 1)

• (-1, 1)

• (1, -1)

• (-1, -1)

What is the y-intercept of the transformed graph after the described transformations?

• 0

• 1

• 7

• 8

In the new example, what is the first step to rewrite the equation in the correct form?

• Multiply by a constant

• Factor out a negative sign

• Switch the positions of terms

• Add a constant to both sides

What happens to the graph when a negative sign is factored out from inside the parentheses?

• The graph flips over the x-axis

• The graph flips over the y-axis

• The graph shifts down

• The graph shifts up

How can we verify that two equations result in the same graph?

• By algebraically manipulating them to the same form

• By comparing their coefficients

• By graphing them on the same axes

• By checking their intercepts

What is the result of raising a negative number to an odd power?

• A positive number

• It depends on the number

• A negative number

• Zero

What does the algebraic verification show about the two equations discussed?

• They are not related

• They have no intercepts

• They have the same graph

• They have different graphs