Exploring Cube Root Functions and Their Transformations

What is the parent function of a cube root typically represented by?

• y = x^3

• y = x^2

• y = 3√x

• y = sqrt(x)

What is the domain of the cube root parent function?

• 1 to infinity

• None of the above

• 0 to infinity

• -infinity to infinity

Which notation is used to express that a value can never reach infinity?

• Square brackets

• Parentheses

• Curly brackets

• Angle brackets

What does a vertical stretch in a cube root function graph indicate?

• The graph becomes wider

• The graph becomes narrower

• The graph becomes taller

• The graph shifts downwards

What transformation does the parameter 'a' in a cube root function control?

• Horizontal shift

• Vertical stretch or compression

• Vertical shift

• Horizontal stretch or compression

If 'H' in a cube root function is negative, in which direction does the graph shift?

• Left

• Right

• Up

• Down

In a transformed cube root function, what does a 'K' value of -1 indicate?

• Shift right by 1 unit

• Shift left by 1 unit

• Shift down by 1 unit

• Shift up by 1 unit

What is the effect of a horizontal compression on a cube root function's graph?

• Makes the graph wider

• Makes the graph narrower

• Makes the graph taller

• Makes the graph shorter

What remains constant in all cube root functions regardless of transformations?

• The asymptotes

• The intercepts

• The domain and range

• The vertex

How does a negative 'a' value affect a cube root function graph?

• Reflects it over the y-axis

• Translates it to the left

• Reflects it over the x-axis

• Translates it to the right