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 to vertically translate a graph?

Back

To vertically translate a graph means to shift it up or down along the y-axis without changing its shape.

Front

What is the effect of replacing f(x) with f(x) + k, where k is a constant?

Back

This transformation results in a vertical translation of the graph of f(x) by k units.

Front

What happens to the graph of f(x) when it is multiplied by a factor greater than 1?

Back

The graph becomes steeper, as it stretches vertically.

Front

What is the parent function of linear equations?

Back

The parent function of linear equations is f(x) = x, which is a straight line through the origin with a slope of 1.

Front

How does a horizontal translation affect the graph of a function?

Back

A horizontal translation shifts the graph left or right along the x-axis.

Front

What is the effect of a negative coefficient in front of f(x)?

Back

A negative coefficient reflects the graph of f(x) across the x-axis.

Front

If f(x) = x, what is the equation of the graph shifted 3 units to the right?

Back

f(x) = x - 3.

Front

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

Back

A graph is less steep when its slope is smaller in absolute value compared to another graph.

Front

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

Back

This transformation makes the graph steeper by a factor of 2.