Parent Function Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, from which other functions can be derived by transformations.

Front

What does a vertical stretch of a function mean?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What does a vertical compression of a function mean?

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.

Front

What transformation does f(x - c) represent?

Back

The graph of the function shifts to the right by c units.

Front

What transformation does f(x + c) represent?

Back

The graph of the function shifts to the left by c units.

Front

What transformation does -f(x) represent?

Back

The graph of the function reflects across the x-axis.

Front

What transformation does f(-x) represent?

Back

The graph of the function reflects across the y-axis.

Front

How does the graph of g(x) = af(x) change if a > 1?

Back

The graph undergoes a vertical stretch.

Front

How does the graph of g(x) = af(x) change if 0 < a < 1?

Back

The graph undergoes a vertical compression.

Front

What does the transformation f(x) + k represent?

Back

The graph of the function shifts vertically by k units; up if k is positive, down if k is negative.