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 shifting a function vertically affect its equation?

Back

Shifting a function vertically affects its equation by adding or subtracting a constant from the function's output.

Front

If f(x) = x, what is the equation of the function shifted down 7 units?

Back

f(x) = x - 7.

Front

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

Back

The transformation g(x) = f(x) - 6 represents a vertical shift of the graph down by 6 units.

Front

Describe the effect of the transformation g(x) = -f(x) on the graph of f(x).

Back

The transformation g(x) = -f(x) reflects the graph of f(x) across the x-axis.

Front

What is a vertical translation in the context of function transformations?

Back

A vertical translation is a shift of the graph of a function up or down without changing its shape.

Front

What is the result of a vertical translation of 2 units up for the function f(x)?

Back

The result is g(x) = f(x) + 2.

Front

How do you represent a reflection across the x-axis in function notation?

Back

A reflection across the x-axis is represented as g(x) = -f(x).

Front

What is the effect of a horizontal shift on the function f(x)?

Back

A horizontal shift moves the graph left or right, changing the input of the function.