Graph Transformations and Properties

The video tutorial explains transformations of the base graph of x cubed, focusing on movements and flips over the x-axis. It demonstrates how to plot transformed points and provides an example of graph transformation with algebraic verification. 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, 1), (2, 4), (-1, -1), (-2, -4)

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

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

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

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

• A flip over the y-axis

• A shift upwards

• A flip over the x-axis

• A shift to the left

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 the transformations?

• (3, 0)

• (1, 0)

• (3, -2)

• (1, -2)

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

• 8

• 6

• 5

• 7

In the new example, what is the first step to put the equation in the proper form?

• Add a constant to both sides

• Switch the positions of terms

• Factor out a negative sign

• Multiply by a constant

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

• The graph shifts upwards

• The graph flips over the x-axis

• The graph flips over the y-axis

• The graph shifts downwards

What is the result of flipping the graph both vertically and horizontally?

• The graph becomes a circle

• The graph rotates 90 degrees

• The graph remains unchanged

• The graph becomes a straight line

How can the algebraic verification show that two equations result in the same graph?

• By analyzing their symmetry

• By checking their intercepts

• By breaking down and comparing their components

• By comparing their slopes

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

• It becomes undefined

• It becomes zero

• It remains negative

• It becomes positive