Transformations of Functions

Front

What is a vertical shift in a function?

Back

A vertical shift occurs when a constant is added to or subtracted from a function, moving it up or down on the graph.

Front

How does the transformation f(x) - 6 affect the graph of f(x)?

Back

It shifts the graph of f(x) down by 6 units.

Front

What does it mean to vertically stretch a function?

Back

A vertical stretch occurs when the function is multiplied by a factor greater than 1, making the graph taller.

Front

Describe the transformation represented by 3h(x).

Back

The graph of h(x) is vertically stretched by a factor of 3.

Front

What is a horizontal shift in a function?

Back

A horizontal shift occurs when a constant is added to or subtracted from the input of the function, moving it left or right on the graph.

Front

How does the transformation f(x + 5) affect the graph of f(x)?

Back

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

Front

How does the transformation f(x - 2) affect the graph of f(x)?

Back

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

Front

What is the effect of multiplying a function by a negative number?

Back

Multiplying a function by a negative number reflects the graph across the x-axis.

Front

What is the general form of a vertical transformation?

Back

The general form is f(x) + k, where k is a constant that shifts the graph vertically.

Front

What is the general form of a horizontal transformation?

Back

The general form is f(x + h) or f(x - h), where h is a constant that shifts the graph horizontally.