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 slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What is the linear parent function?

Back

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

Front

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

Back

The graph becomes steeper by that factor.

Front

What is the effect of adding a constant to a function, such as f(x) + c?

Back

Adding a constant c shifts the graph vertically by c units.

Front

What is the effect of subtracting a constant from a function, such as f(x) - c?

Back

Subtracting a constant c shifts the graph vertically down by c units.

Front

What does g(x) = -f(x) represent?

Back

It represents a reflection of the graph of f(x) across the x-axis.

Front

What does g(x) = f(-x) represent?

Back

It represents a reflection of the graph of f(x) across the y-axis.

Front

How does the graph of f(x) = mx + b change if m is negative?

Back

The graph will slope downwards from left to right.

Front

What is the effect of multiplying a function by a negative number, such as g(x) = -f(x)?

Back

It reflects the graph across the x-axis.