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 transformations?

Back

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

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x) - 6?

Back

The graph of g(x) is shifted down 6 units.

Front

Describe the transformation when g(x) = f(x) + 3 is applied to the parent function f(x) = x.

Back

The graph of g(x) is shifted up 3 units.

Front

What does it mean when a graph is less steep by a factor of 1/5?

Back

It means that the slope of the graph is reduced to one-fifth of its original steepness.

Front

If the graph of f(x) = x is shifted down 7 units, what is the equation of the new graph?

Back

The new graph is represented by g(x) = f(x) - 7.

Front

What is a vertical translation in the context of graph transformations?

Back

A vertical translation moves the graph up or down without changing its shape.

Front

What is a horizontal translation in the context of graph transformations?

Back

A horizontal translation moves the graph left or right without changing its shape.

Front

What does it mean for a graph to be reflected over the x-axis?

Back

A reflection over the x-axis means that for every point (x, y) on the graph, the point (x, -y) is also on the graph.

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.