Review: 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) = 3x + 5 differ from its parent function?

Back

The graph is steeper due to the coefficient 3 and is shifted up 5 units.

Front

What does it mean to shift a graph down by 6 units?

Back

It means that every point on the graph of the function is moved down 6 units on the y-axis.

Front

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

Back

It reflects the graph of the function across the x-axis.

Front

What does the transformation g(x) = f(x) + 3 represent?

Back

It represents a vertical shift of the graph of f(x) upwards by 3 units.

Front

What is the result of the transformation g(x) = -f(x) + 2?

Back

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

Front

If g(x) = 2f(x), what happens to the graph of f(x)?

Back

The graph is vertically stretched by a factor of 2.

Front

What does the transformation 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 effect of the transformation g(x) = f(x) - 3?

Back

It shifts the graph of f(x) down by 3 units.