Transformations of Cube Root Functions

This video tutorial explains how to graph a cube root function with horizontal and vertical shifts, as well as a reflection. It begins with setting up initial x and y values, then demonstrates how to apply a horizontal shift by adjusting x values. The tutorial continues with a vertical shift and reflection, modifying y values accordingly. Finally, it shows how to calculate and plot the transformed points on a graph.

What transformations are applied to the cube root function in this example?

• Horizontal shift only

• Vertical shift only

• Reflection only

• Horizontal and vertical shifts with reflection

What is the first step in graphing a cube root function?

• Plot the points

• Reflect the graph

• Set initial x and y values

• Apply vertical shifts

How do you determine the transformation for x values in a cube root function?

• Multiply by the value inside the radical

• Divide by the value inside the radical

• Subtract the value inside the radical

• Add the value inside the radical

What is the result of subtracting 2 from the x value of -8?

• -12

• -6

• -10

• -4

What is the effect of a vertical shift on the y values?

• It divides y values by a constant

• It subtracts a constant from y values

• It multiplies y values by a constant

• It adds a constant to y values

How does reflection affect the y values in this function?

• It adds 3 to y values

• It divides y values by -1

• It multiplies y values by -1

• It subtracts 3 from y values

What is the new y value after applying reflection and vertical shift to -2?

• 0

• 1

• -1

• -3

What is the final step in graphing the cube root function?

• Apply horizontal shifts

• Apply vertical shifts

• Plot the points and connect them

• Reflect the graph

Which point is plotted after applying all transformations to the original point (0, 0)?

• (-2, -3)

• (-1, -4)

• (0, -3)

• (1, -2)

What should the graph look like after connecting all the transformed points?

• A zigzag pattern

• A cubic curve

• A parabola

• A straight line