Cubic and Cube Root Functions Activity For Exemplar Lesson

Front

What is a cubic function?

Back

A cubic function is a polynomial function of degree three, typically expressed in the form f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and a ≠ 0.

Front

What is a cube root function?

Back

A cube root function is a function that involves the cube root of a variable, typically expressed as f(x) = ∛(x). It is the inverse of the cubic function.

Front

How does the graph of f(x) = x^3 transform to f(x) = - (x + 3)^3 + 2?

Back

The graph is transformed 3 units left, 2 units up, and reflected across the x-axis.

Front

What effect does reflecting a function over the x-axis have?

Back

Reflecting a function over the x-axis changes the sign of the output values, resulting in a vertical flip of the graph.

Front

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

Back

Vertically compressing a function by a factor of 1/4 means that all output values of the function are multiplied by 1/4, making the graph closer to the x-axis.

Front

What is the solution to the equation ∛(x) = 3?

Back

The solution is x = 27, since 3^3 = 27.

Front

What is the solution to the equation ∛(x) = 10?

Back

The solution is x = 1000, since 10^3 = 1000.

Front

What type of function is represented by the graph of f(x) = ∛(x)?

Back

The graph represents a cube root function.

Front

What is the general form of a cube root function?

Back

The general form of a cube root function is f(x) = a ∛(x - h) + k, where (h, k) is the translation of the graph.

Front

How do you shift a cube root function left by 9 units?

Back

To shift the function left by 9 units, you replace x with (x + 9) in the function's equation.