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 functions?

Back

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

Front

How does the function g(x) = f(x) - 2 transform the parent function?

Back

g(x) is shifted down 2 units.

Front

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

Back

g(x) is shifted left 3 units.

Front

What is the effect of the transformation g(x) = f(x) + 3 on the parent function?

Back

g(x) is shifted up 3 units.

Front

How can you determine if a function is linear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b, where m and b are constants.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; it represents how much y changes for a unit change in x.

Front

What does it mean for a function to be non-linear?

Back

A non-linear function cannot be expressed in the form f(x) = mx + b and does not have a constant rate of change.

Front

What is the transformation represented by g(x) = f(x) - 6?

Back

g(x) is shifted down 6 units.

Front

What is the graphical representation of a linear function?

Back

The graphical representation of a linear function is a straight line.