Vertical and Horizontal Stretches and Compressions

Front

What is a vertical stretch?

Back

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

Front

What is a vertical compression?

Back

A vertical compression occurs when a function is multiplied by a factor between 0 and 1, making the graph shorter.

Front

What is a horizontal stretch?

Back

A horizontal stretch occurs when the input of a function is multiplied by a factor between 0 and 1, making the graph wider.

Front

What is a horizontal compression?

Back

A horizontal compression occurs when the input of a function is multiplied by a factor greater than 1, making the graph narrower.

Front

How does the equation y = f(x - h) + k transform the graph of f(x)?

Back

It shifts the graph horizontally by h units and vertically by k units.

Front

What does the transformation y = af(x) do when |a| > 1?

Back

It vertically stretches the graph of f(x).

Front

What does the transformation y = af(x) do when 0 < |a| < 1?

Back

It vertically compresses the graph of f(x).

Front

What does the transformation y = f(bx) do when |b| > 1?

Back

It horizontally compresses the graph of f(x).

Front

What does the transformation y = f(bx) do when 0 < |b| < 1?

Back

It horizontally stretches the graph of f(x).

Front

If f(x) = x^2, what is g(x) = f(3x)?

Back

g(x) = (3x)^2 = 9x^2, which is a horizontal compression.