Transformations of Polynomial Functions

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What is the parent function of a quadratic polynomial?

Back

The parent function of a quadratic polynomial is f(x) = x².

Front

What does it mean for a graph to narrow or widen?

Back

A graph narrows when the coefficient of the leading term is greater than 1, and widens when it is between 0 and 1.

Front

What is a vertical stretch in the context of polynomial functions?

Back

A vertical stretch occurs when the coefficient of the function is greater than 1, making the graph steeper.

Front

What is a horizontal shift in polynomial functions?

Back

A horizontal shift occurs when the input variable x is replaced by (x - h) or (x + h), shifting the graph left or right.

Front

What does a reflection over the y-axis indicate?

Back

A reflection over the y-axis indicates that the function f(x) is transformed to f(-x).

Front

How does a vertical shift affect the graph of a polynomial function?

Back

A vertical shift moves the graph up or down by adding or subtracting a constant from the function.

Front

What is the effect of a negative coefficient in front of a function?

Back

A negative coefficient reflects the graph over the x-axis.

Front

What does it mean to shift a graph to the left?

Back

Shifting a graph to the left means replacing x with (x + h) in the function, where h is a positive number.

Front

What is the transformation of the function y = g(x - 3)?

Back

The transformation shifts the graph of g(x) to the right by 3 units.