24-25 Alg1 3-7 FLASHCARD - 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 it mean for a graph to be a reflection?

Back

A reflection of a graph across a line (usually the x-axis or y-axis) means that for every point (x, y) on the original graph, there is a corresponding point (x, -y) or (-x, y) on the reflected graph.

Front

How does the graph of g(x) = -f(x) + 2 transform the graph of f(x)?

Back

This transformation reflects the graph of f(x) across the x-axis and then shifts it up 2 units.

Front

What is the effect of a vertical shrink on a graph?

Back

A vertical shrink compresses the graph towards the x-axis, making it less steep.

Front

What does the equation g(x) = f(x - 4) do to the graph of f(x)?

Back

It shifts the graph of f(x) to the right by 4 units.

Front

What is the parent function of a linear equation?

Back

The parent function of a linear equation is y = x, which represents a straight line through the origin with a slope of 1.

Front

How does the transformation g(x) = 1/2f(x) affect the graph of f(x)?

Back

It vertically shrinks the graph of f(x) by a factor of 1/2.

Front

What does it mean for a graph to be steeper?

Back

A graph is steeper if it has a greater slope, meaning it rises or falls more quickly as you move along the x-axis.

Front

What is the effect of shifting a graph up by 5 units?

Back

Shifting a graph up by 5 units means that every point on the graph is moved vertically upwards by 5 units.

Front

What does the transformation g(x) = -f(x) indicate about the graph of f(x)?

Back

This transformation reflects the graph of f(x) across the x-axis.