Cubic and Cube Root Transformations

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

How many x-intercepts can a cubic function have?

Back

A cubic function can have 1, 2, or 3 x-intercepts.

Front

What is the parent function of cubic functions?

Back

The parent function of cubic functions is f(x) = x^3.

Front

What does it mean to translate a function left 4 units?

Back

Translating a function left 4 units means to replace x with (x + 4) in the function's equation.

Front

What is a vertical stretch in transformations?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What is a horizontal compression in transformations?

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor greater than 1, making the graph narrower.

Front

How do you identify the transformation of g(x) = (x - 1)^3?

Back

This function represents a horizontal translation to the right by 1 unit of the parent function f(x) = x^3.

Front

What is the effect of a vertical shift down by 4 on a cubic function?

Back

A vertical shift down by 4 means subtracting 4 from the function, resulting in f(x) = x^3 - 4.

Front

What is the general form of a cubic function?

Back

The general form of a cubic function is f(x) = ax^3 + bx^2 + cx + d.

Front

What is the significance of the leading coefficient in a cubic function?

Back

The leading coefficient (a) determines the direction of the graph's ends: if a > 0, the graph rises to the right; if a < 0, it falls to the right.