Linear Transformation Retake 11/19

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 effect does the transformation h(x) = f(x) - 5 have on the graph of f(x)?

Back

It shifts the graph of f(x) down by 5 units.

Front

What does the transformation g(x) = f(x) + 2 do to the graph of f(x)?

Back

It shifts the graph of f(x) up by 2 units.

Front

How does the transformation h(x) = 2f(x) - 5 affect the steepness of the graph?

Back

It makes the graph steeper and shifts it down by 5 units.

Front

What is the effect of the transformation h(x) = f(1/4 x) on the graph of f(x)?

Back

It makes the graph less steep (wider) by a factor of 4.

Front

What does the transformation g(x) = f(x - 3) do to the graph of f(x)?

Back

It shifts the graph of f(x) to the right by 3 units.

Front

What is the general form of a vertical shift in a function?

Back

A vertical shift can be represented as f(x) + k, where k is the number of units to shift up (if k > 0) or down (if k < 0).

Front

What is the general form of a horizontal shift in a function?

Back

A horizontal shift can be represented as f(x - h), where h is the number of units to shift right (if h > 0) or left (if h < 0).

Front

What does multiplying a function by a constant do to its graph?

Back

Multiplying a function by a constant greater than 1 makes the graph steeper, while multiplying by a constant between 0 and 1 makes it less steep.

Front

What is the effect of a negative constant in front of a function?

Back

A negative constant reflects the graph across the x-axis.