Linear Transformations

Front

What is a linear transformation?

Back

A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

Front

What does a horizontal translation of a graph involve?

Back

A horizontal translation involves shifting the graph left or right along the x-axis without changing its shape.

Front

How does a vertical translation affect a graph?

Back

A vertical translation shifts the graph up or down along the y-axis, affecting the y-values of the function.

Front

What is the effect of reflecting a graph over the x-axis?

Back

Reflecting a graph over the x-axis inverts the y-values of the function, resulting in a mirror image across the x-axis.

Front

What does it mean to stretch a graph vertically?

Back

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

Front

What is the transformation represented by f(x) = x + c?

Back

The transformation f(x) = x + c represents a vertical translation of the graph of f(x) by c units.

Front

What is the transformation represented by f(x) = x - d?

Back

The transformation f(x) = x - d represents a vertical translation of the graph of f(x) down by d units.

Front

How do you represent a horizontal shift of a graph to the left?

Back

A horizontal shift to the left is represented by f(x) = f(x + c), where c is a positive constant.

Front

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

Back

Multiplying a function by a negative scalar reflects the graph over the x-axis and scales it vertically.

Front

What does the equation y = mx + b represent in terms of transformations?

Back

The equation y = mx + b represents a linear function where m is the slope and b is the y-intercept, indicating vertical and horizontal transformations.