Cubic & Cube Root Transformations

Front

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

Back

(-∞, ∞)

Front

What is the range of the function f(x) = ∛(x)?

Back

(-∞, ∞)

Front

What transformation occurs when a function is reflected over the x-axis?

Back

The output values of the function are negated.

Front

If f(x) = ∛(x) is vertically compressed by a factor of 1/4, what is the new function?

Back

f(x) = (1/4)∛(x)

Front

What does it mean for a function to be shifted right by 5 units?

Back

The input values of the function are increased by 5.

Front

What is the effect of a vertical stretch by a factor of 2 on the function f(x)?

Back

The output values of the function are multiplied by 2.

Front

If f(x) = -2√(x-5), what transformations are applied compared to the parent function?

Back

Reflected over the x-axis, vertical stretch by 2, and shifted right 5.

Front

What is the domain of the function f(x) = -√(x-1) + 4?

Back

[1, ∞)

Front

What is the range of the function f(x) = -√(x-1) + 4?

Back

(-∞, 4]

Front

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

Back

f(x) = ∛(x + 9)