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 linear parent function?

Back

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

Front

If f(x) = x is shifted down 6 units, what is the new function?

Back

g(x) = f(x) - 6, which simplifies to g(x) = x - 6.

Front

What effect does multiplying a function by a fraction have on its steepness?

Back

Multiplying a function by a fraction less than 1 makes it less steep.

Front

What is the slope of the line represented by the function y = 3x + 8?

Back

The slope is 3.

Front

If the function f(x) = x is transformed to g(x) = 2f(x), what is the transformation?

Back

The transformation is a vertical stretch by a factor of 2.

Front

What happens to the graph of f(x) = x when it is replaced with f(x) + 4?

Back

The graph shifts up 4 units.

Front

Identify the transformation: g(x) = f(x + 3).

Back

The graph shifts left 3 units.

Front

What is the effect of replacing f(x) with f(x) - 2?

Back

The graph shifts down 2 units.

Front

If f(x) = x and g(x) = -f(x), what transformation occurs?

Back

The graph reflects over the x-axis.