Polynomial Transformations

Front

What is a polynomial transformation?

Back

A polynomial transformation refers to the changes made to the graph of a polynomial function through operations such as translations, reflections, stretches, and compressions.

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 the transformation f(x) = -x^3 affect the graph of f(x) = x^3?

Back

The transformation f(x) = -x^3 reflects the graph of f(x) = x^3 across the x-axis.

Front

What is the effect of adding a positive constant to a polynomial function?

Back

Adding a positive constant to a polynomial function translates the graph upward by that constant value.

Front

What is the effect of subtracting a positive constant from a polynomial function?

Back

Subtracting a positive constant from a polynomial function translates the graph downward by that constant value.

Front

What does the transformation f(x) = (x - 4)^2 represent?

Back

The transformation f(x) = (x - 4)^2 represents a horizontal translation of the graph of f(x) = x^2 to the right by 4 units.

Front

What does the transformation f(x) = (x + 3)^2 represent?

Back

The transformation f(x) = (x + 3)^2 represents a horizontal translation of the graph of f(x) = x^2 to the left by 3 units.

Front

What is the effect of multiplying a polynomial function by a negative constant?

Back

Multiplying a polynomial function by a negative constant reflects the graph across the x-axis and may also stretch or compress it depending on the absolute value of the constant.

Front

What does it mean to stretch a graph vertically?

Back

Stretching a graph vertically means that the y-values of the function are multiplied by a factor greater than 1, making the graph taller.