Vertical Stretches and Compressions

Front

What is a vertical stretch in a function?

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 in a function?

Back

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

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

How does the graph of f(x) = |x| change when it is vertically stretched by a factor of 2?

Back

The new function is g(x) = 2|x|, which makes the graph taller.

Front

How does the graph of f(x) = x^2 change when it is vertically compressed by a factor of 1/2?

Back

The new function is g(x) = (1/2)x^2, which makes the graph shorter.

Front

What transformation occurs in the function h(x) = (1/3)(x - 2)^2 + 1?

Back

The graph is translated right 2 units, vertically compressed by a factor of 1/3, and translated up 1 unit.

Front

What does the equation y = (x + 4)^2 represent in terms of transformations?

Back

The graph is translated left 4 units.

Front

What is the effect of a negative sign in front of a function, such as y = -f(x)?

Back

It reflects the graph across the x-axis.

Front

If f(x) = x^2, what is the equation for a vertical stretch by a factor of 3?

Back

g(x) = 3x^2.

Front

What is the transformation of the function y = (x - 1)^2 - 5?

Back

The graph is translated right 1 unit and down 5 units.