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 is the parent function of linear equations?

Back

The parent function of linear equations is f(x) = x.

Front

How does the graph of f(x) = x shift when transformed to g(x) = f(x) + c?

Back

The graph shifts vertically by c units; if c is positive, it shifts up, and if c is negative, it shifts down.

Front

How does the graph of f(x) = x shift when transformed to g(x) = f(x - c)?

Back

The graph shifts horizontally; if c is positive, it shifts right, and if c is negative, it shifts left.

Front

What does it mean for a graph to be reflected?

Back

A reflection means that the graph is flipped over a specific line, such as the x-axis or y-axis.

Front

What is the effect of adding a positive number to the function f(x)?

Back

Adding a positive number shifts the graph of the function upward.

Front

What is the effect of subtracting a positive number from the function f(x)?

Back

Subtracting a positive number shifts the graph of the function downward.

Front

What happens to the graph of f(x) = x when transformed to g(x) = f(x + 3)?

Back

The graph shifts left by 3 units.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions do not have a constant rate of change and can graph as curves.

Front

How does the equation y = (x) + 7 transform the parent function?

Back

It shifts the graph of the parent function up by 7 units.