Transformations of Root Functions

The video tutorial explains how to transform graphs of functions through a series of steps. It begins with the square root function, demonstrating how to flip it over the y-axis, scale it by multiplying by 2, and shift it downward. The tutorial then moves on to a similar transformation process for the cube root function, including horizontal shifts and vertical flips. The instructor encourages viewers to pause and attempt the transformations independently before following along with the guided solutions.

What is the initial step in identifying the graph of y = 2√(-x - 1)?

• Draw the graph of y = 2x

• Draw the graph of y = x^2

• Draw the graph of y = √x

• Draw the graph of y = -x

How does the graph of y = √x change when transformed to y = √(-x)?

• It shifts upwards

• It flips over the y-axis

• It shifts to the right

• It flips over the x-axis

What effect does multiplying by 2 have on the graph of y = √(-x)?

• It shifts the graph to the left

• It compresses the graph

• It stretches the graph vertically

• It flips the graph over the x-axis

What is the final transformation applied to the graph of y = 2√(-x) to get y = 2√(-x - 1)?

• Shift the graph up by 1

• Shift the graph down by 1

• Shift the graph left by 1

• Shift the graph right by 1

Which of the following graphs represents y = 2√(-x - 1) correctly?

• Graph B

• Graph A

• Graph D

• Graph C

In the cube root problem, what is the first transformation applied to y = ∛x?

• Shift the graph down by 2

• Shift the graph right by 2

• Shift the graph left by 2

• Shift the graph up by 2

What happens to the graph of y = ∛(x + 2) when multiplied by -1?

• It shifts to the right

• It flips over the x-axis

• It flips over the y-axis

• It shifts upwards

What is the final transformation applied to the graph of y = -∛(x + 2) to get y = -∛(x + 2) + 5?

• Shift the graph up by 5

• Shift the graph right by 5

• Shift the graph down by 5

• Shift the graph left by 5

Which point is crucial to identify the correct graph of y = -∛(x + 2) + 5?

• (0, 5)

• (0, 0)

• (-2, 5)

• (-2, 0)

What is the effect of adding 5 to the graph of y = -∛(x + 2)?

• It shifts the graph down by 5

• It shifts the graph up by 5

• It shifts the graph left by 5

• It shifts the graph right by 5