Linear Transformations and Parent Function

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

f(x) = x

Front

How does the equation y = (x - 3) + 5 transform the parent function?

Back

It shifts the graph 3 units to the right and 5 units up.

Front

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

Back

g(x) is shifted left 3 units.

Front

What does the transformation g(x) = f(x + 6) represent?

Back

g(x) is shifted left 6 units.

Front

Which function represents the parent function shifted down two units?

Back

f(x) = x - 2

Front

What is the effect of adding a positive number to the input of a function?

Back

It shifts the graph to the left.

Front

What is the effect of subtracting a positive number from the input of a function?

Back

It shifts the graph to the right.

Front

What happens to the graph of f(x) = x when you replace it with f(x) = x + b, where b is positive?

Back

The graph shifts up by b units.

Front

What happens to the graph of f(x) = x when you replace it with f(x) = x - b, where b is positive?

Back

The graph shifts down by b units.