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 equations?

Back

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

Front

What happens to the graph of f(x) = x when it is transformed to g(x) = f(x) - 7?

Back

The graph is shifted vertically down by 7 units.

Front

If the graph of f(x) = x is shifted 7 units up and 5 units left, what is the new function?

Back

f(x) = (x + 5) + 7.

Front

What is the effect of shifting the graph of f(x) = x down by 7 units?

Back

The new function is f(x) = x - 7.

Front

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

Back

g(x) is shifted down 6 units.

Front

Is the function f(x) = x^2 linear or nonlinear?

Back

Nonlinear.

Front

What is the general form of a linear function?

Back

A linear function can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that the function is increasing.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that the function is decreasing.