Transformations: Stretches and Compressions

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller. For example, if g(x) = 2f(x), the function f(x) is vertically stretched by a factor of 2.

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter. For example, if g(x) = (1/2)f(x), the function f(x) is vertically compressed by a factor of 1/2.

Front

What does the transformation g(x) = f(2x) represent?

Back

This transformation represents a horizontal compression of the function f(x) by a factor of 1/2.

Front

What does the transformation g(x) = f(1/2 x) represent?

Back

This transformation represents a horizontal stretch of the function f(x) by a factor of 2.

Front

How does the transformation g(x) = f(x) + 2 affect the graph of f(x)?

Back

This transformation shifts the graph of f(x) vertically upwards by 2 units.

Front

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

Back

This transformation shifts the graph of f(x) horizontally to the right by 2 units.

Front

What is the effect of the transformation g(x) = 3f(x)?

Back

This transformation results in a vertical stretch of the function f(x) by a factor of 3.

Front

What is the effect of the transformation g(x) = (1/3)f(x)?

Back

This transformation results in a vertical compression of the function f(x) by a factor of 1/3.

Front

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

Back

This transformation represents a horizontal compression of the function f(x) by a factor of 1/6.

Front

What does the transformation g(x) = f(x + 3) represent?

Back

This transformation shifts the graph of f(x) horizontally to the left by 3 units.