Unit 7: Cube Root Equations and Transformations

Front

What is the domain of all cube root functions in interval notation?

Back

(−∞,∞)

Front

What is the general form of a cube root function?

Back

y = ∛(x) or y = a∛(x - h) + k, where (h, k) is the translation.

Front

How does the graph of y = ∛(x) differ from y = (x - 1)³?

Back

y = ∛(x) is a cube root function, while y = (x - 1)³ is a cubic function.

Front

What transformations occur when the function f(x) = ∛(x) is reflected over the x-axis?

Back

The output values of the function are negated, resulting in f(x) = -∛(x).

Front

What does it mean to vertically compress a function by a factor of 1/4?

Back

The output values of the function are multiplied by 1/4, making the graph flatter.

Front

If f(x) = ∛(x) is shifted left by 9 units, what is the new equation?

Back

f(x) = ∛(x + 9).

Front

What is the effect of shifting a function down by 1 unit?

Back

The output values are decreased by 1, resulting in f(x) = ∛(x) - 1.

Front

How do you identify the graph of a cube root function?

Back

A cube root function has a characteristic shape that increases slowly and passes through the origin.

Front

What is the equation for the red function given in the quiz?

Back

y = (x - 1)³.

Front

What is the equation for the function that is reflected over the x-axis, vertically compressed by 1/4, and shifted left 9?

Back

f(x) = -1/4 ∛(x + 9).