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 effect does shifting a graph down by 'k' units have on its equation?

Back

Shifting a graph down by 'k' units results in subtracting 'k' from the function's output, changing the equation to f(x) = f(x) - k.

Front

How does reflecting a graph over the x-axis affect its equation?

Back

Reflecting a graph over the x-axis changes the equation to f(x) = -f(x), inverting the sign of the output.

Front

What does it mean for a graph to be less steep?

Back

A graph is less steep when its slope is reduced, which can be represented by multiplying the x variable by a factor less than 1.

Front

If the parent function is f(x) = x, what is the equation after shifting it down 7 units?

Back

The new equation after shifting down 7 units is f(x) = x - 7.

Front

What is the transformation represented by the equation f(x) = 2x?

Back

The transformation represented by f(x) = 2x is a vertical stretch by a factor of 2.

Front

What does it mean for a graph to be a reflection?

Back

A reflection in graphing refers to flipping the graph over a specified axis, such as the x-axis or y-axis.

Front

How can you describe a vertical shift of a graph?

Back

A vertical shift of a graph occurs when the entire graph moves up or down without changing its shape.

Front

What is the effect of multiplying a function by a factor greater than 1?

Back

Multiplying a function by a factor greater than 1 results in a vertical stretch of the graph.

Front

What is the transformation when a graph is shifted up by 'k' units?

Back

Shifting a graph up by 'k' units results in adding 'k' to the function's output, changing the equation to f(x) = f(x) + k.