Transformations of Functions

Front

What is a horizontal shift in a function?

Back

A horizontal shift occurs when the input of the function is adjusted by adding or subtracting a constant value, moving the graph left or right.

Front

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

Back

The transformation f(x + c) represents a horizontal shift of the graph of f(x) to the left by c units.

Front

What does the transformation f(x - c) represent?

Back

The transformation f(x - c) represents a horizontal shift of the graph of f(x) to the right by c units.

Front

What is a vertical shift in a function?

Back

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

Front

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

Back

The transformation f(x) + k represents a vertical shift of the graph of f(x) upward by k units.

Front

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

Back

The transformation f(x) - k represents a vertical shift of the graph of f(x) downward by k units.

Front

What is a vertical stretch in a function?

Back

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

Front

What does the transformation a * f(x) represent when a > 1?

Back

The transformation a * f(x) represents a vertical stretch of the graph of f(x) by a factor of a.

Front

What does the transformation a * f(x) represent when 0 < a < 1?

Back

The transformation a * f(x) represents a vertical compression of the graph of f(x) by a factor of a.

Front

What is a horizontal stretch in a function?

Back

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