Transformations of Cube Root Functions

Mrs. Ga introduces cube root functions, highlighting their differences from square root functions, particularly in handling negative values. The video covers transformations such as reflection, vertical stretch, and horizontal shifts, and demonstrates how to graph these transformations. Students are encouraged to practice graphing by identifying transformations and applying them to the parent function.

What is the first step in graphing cube root functions as mentioned in the introduction?

• Memorize the function's formula.

• Complete a T-chart for the function.

• Draw the graph directly.

• Calculate the function's derivative.

What is the domain of the cube root function?

• All positive numbers

• Only integers

• All negative numbers

• All real numbers

Why can cube root functions have negative x-values?

• Because cube roots of negative numbers are complex.

• Because cube roots of negative numbers are real.

• Because cube roots of negative numbers are imaginary.

• Because cube roots of negative numbers are undefined.

What is the effect of a negative sign in front of a cube root function?

• It causes a vertical stretch.

• It causes a horizontal stretch.

• It causes a vertical reflection.

• It causes a horizontal reflection.

What does a horizontal translation involve?

• Reflecting the graph over the x-axis.

• Shifting the graph up or down.

• Shifting the graph left or right.

• Reflecting the graph over the y-axis.

In describing transformations, what should be addressed first?

• Domain and range

• Vertical shifts

• Reflections, stretches, or shrinks

• Horizontal shifts

How do you identify a vertical stretch in an equation?

• By looking for a negative sign.

• By identifying a value greater than one multiplied in front.

• By looking for a horizontal shift.

• By identifying a value less than one multiplied in front.

What is the starting point for the parent cube root function?

• (0, 0)

• (2, 2)

• (1, 1)

• (-1, -1)

What should be done first when graphing a function with multiple transformations?

• Apply shifts first.

• Apply reflections, stretches, or shrinks first.

• Draw the graph without transformations.

• Calculate the derivative.

In the practice problems, what is the first transformation applied?

• Vertical stretch

• Horizontal shift

• Reflection

• Vertical shift