Cubic & 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

What is the cube root of a number?

Back

The cube root of a number x is a value y such that y^3 = x. It is denoted as ∛x.

Front

What does a vertical stretch by a factor of k mean?

Back

A vertical stretch by a factor of k means that the y-values of the function are multiplied by k, making the graph taller.

Front

What does a vertical shrink by a factor of k mean?

Back

A vertical shrink by a factor of k means that the y-values of the function are multiplied by 1/k, making the graph shorter.

Front

What is a translation of a graph?

Back

A translation of a graph involves shifting the graph horizontally or vertically without changing its shape.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What does it mean to reflect a graph over the y-axis?

Back

Reflecting a graph over the y-axis means that for every point (x, y) on the graph, the point (-x, y) will also be on the graph.

Front

How does a translation right by h units affect the graph of a function?

Back

A translation right by h units shifts the graph of the function to the right by h units, changing the function to f(x - h).

Front

How does a translation down by k units affect the graph of a function?

Back

A translation down by k units shifts the graph of the function down by k units, changing the function to f(x) - k.

Front

What is the effect of a horizontal compression by a factor of k?

Back

A horizontal compression by a factor of k means that the x-values of the function are divided by k, making the graph narrower.