Transformations of Polynomial Functions

Front

What is a transformation of a polynomial function?

Back

A transformation of a polynomial function refers to any change made to the function's graph, including shifts, stretches, compressions, and reflections.

Front

How does shifting a function to the right affect its equation?

Back

To shift a function to the right by 'h' units, replace 'x' with '(x - h)' in the function's equation.

Front

How does shifting a function to the left affect its equation?

Back

To shift a function to the left by 'h' units, replace 'x' with '(x + h)' in the function's equation.

Front

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

Back

Adding a constant 'k' to a polynomial function translates the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

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

Back

Multiplying a polynomial function by a negative number reflects the graph across the x-axis.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you represent a vertical stretch of a polynomial function?

Back

To represent a vertical stretch by a factor of 'k', multiply the function by 'k'. For example, f(x) becomes k*f(x).

Front

What is the equation for a cubic function shifted up by 2 units?

Back

The equation for a cubic function f(x) = x^3 shifted up by 2 units is g(x) = x^3 + 2.

Front

What does the vertex form of a quadratic function look like?

Back

The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How do you translate a quadratic function down by 4 units?

Back

To translate a quadratic function down by 4 units, subtract 4 from the function: f(x) = x^2 becomes g(x) = x^2 - 4.