Linear Tranformations

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 effect of the transformation g(x) = f(x - 7) on the graph of f(x)?

Back

The graph of f(x) is shifted horizontally to the right by 7 units.

Front

What does a vertical shift of a graph entail?

Back

A vertical shift moves the graph up or down without changing its shape.

Front

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

Back

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

Front

What is the transformation of g(x) = f(x + 2)?

Back

The graph of f(x) is shifted horizontally to the left by 2 units.

Front

How does a downward shift affect the graph of a function?

Back

A downward shift moves the graph down by a specified number of units.

Front

What is the result of shifting the graph of f(x) = x down by 3 units?

Back

The new function is f(x) = x - 3.

Front

What does the notation f(x) = f(x - a) represent?

Back

This notation represents a horizontal shift of the graph of f(x) to the right by 'a' units.

Front

What is the transformation of g(x) = f(x) + k?

Back

The graph of f(x) is shifted vertically by 'k' units; if k is positive, it shifts up, and if k is negative, it shifts down.

Front

If a graph is shifted 5 units left and 7 units up, what is the transformation in function notation?

Back

The transformation can be represented as f(x) = f(x + 5) + 7.