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 + 3) transform the parent function f(x) = x?

Back

g(x) is shifted left 3 units.

Front

How does the function g(x) = f(x) + 3 transform the parent function f(x) = x?

Back

g(x) is shifted up 3 units.

Front

Which function represents the parent function shifted down two units?

Back

f(x) = x - 2.

Front

Is the function f(x) = x^2 Linear or Nonlinear?

Back

Nonlinear.

Front

What is the effect of adding a constant to a linear function?

Back

Adding a constant shifts the graph vertically.

Front

What is the effect of adding a term inside the function (e.g., f(x + c))?

Back

It shifts the graph horizontally.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are constants.