Transformations of Cubic Functions

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 concludes with algebraic verification of the transformations, ensuring the graph's accuracy.

What is the base graph for the function y = x^3?

• A straight line

• A parabola

• A circle

• A cubic curve

Which of the following points is NOT a key point on the base graph of y = x^3?

• (3, 9)

• (0, 0)

• (2, 8)

• (1, 1)

What does a negative sign outside the function y = x^3 indicate?

• A reflection over the x-axis

• A reflection over the y-axis

• A horizontal shift

• A vertical shift

If the function y = (x - 2)^3 is given, in which direction is the graph shifted?

• 2 units up

• 2 units to the right

• 2 units to the left

• 2 units down

What is the new origin after shifting the graph of y = x^3 two units to the right and one unit down?

• (-2, 1)

• (1, -2)

• (2, -1)

• (0, 0)

How does the graph of y = -x^3 differ from y = x^3?

• It is reflected over the x-axis

• It is reflected over the y-axis

• It is shifted down

• It is shifted up

When plotting the transformed graph, what is the first step after determining the new origin?

• Identifying key points

• Plotting the intercepts

• Drawing the original graph

• Applying the reflection

What is the y-intercept of the transformed graph after shifting and reflecting?

• 7

• 0

• 1

• 8

In the new example, what is the first step to rewrite the equation for transformation?

• Multiply by a constant

• Switch the positions of terms

• Factor out a negative

• Add a constant

What happens to the graph when a negative sign is inside the parentheses of y = (-x)^3?

• It shifts left

• It shifts right

• It reflects over the y-axis

• It reflects over the x-axis