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 = -(x - 2)² + 4 transform the basic quadratic function y = x²?

Back

The equation reflects the graph over the x-axis, shifts it right 2 units, and shifts it up 4 units.

Front

What is the effect of a vertical stretch on a function?

Back

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

Front

What is the effect of a vertical compression on a function?

Back

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

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

How do you identify the vertex of the function y = a(x - h)² + k?

Back

The vertex of the function is the point (h, k), where h is the horizontal shift and k is the vertical shift.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants.