Transformation of Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to the changes made to the graph of a function, including shifts, reflections, stretches, and compressions.

Front

What does it mean to shift a function vertically?

Back

Shifting a function vertically means moving the graph up or down without changing its shape. This is done by adding or subtracting a constant from the function.

Front

What does it mean to shift a function horizontally?

Back

Shifting a function horizontally means moving the graph left or right. This is achieved by adding or subtracting a constant from the variable inside the function.

Front

What is a reflection in the context of function transformations?

Back

A reflection is a transformation that flips the graph of a function over a specific axis, such as the x-axis or y-axis.

Front

How does the equation y = -f(x) affect the graph of f(x)?

Back

The equation y = -f(x) reflects the graph of f(x) over the x-axis.

Front

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

Back

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

Front

What is a vertical stretch?

Back

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

Front

What is a vertical compression?

Back

A vertical compression occurs when the output of a function is multiplied by a factor between 0 and 1, making the graph shorter.

Front

What is the standard form of a quadratic function?

Back

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

Front

What does the vertex of a parabola represent?

Back

The vertex of a parabola represents the highest or lowest point of the graph, depending on whether it opens upwards or downwards.