Transformations of Functions

Front

What is a transformation of a function?

Back

A transformation of a function is an operation that alters the graph of the function in some way, such as shifting, reflecting, stretching, or compressing.

Front

What does a translation of a function mean?

Back

A translation of a function means shifting the graph of the function horizontally and/or vertically without changing its shape.

Front

What is the effect of a positive value added to a function, f(x) + k?

Back

Adding a positive value k to f(x) shifts the graph of the function upward by k units.

Front

What is the effect of a negative value added to a function, f(x) - k?

Back

Subtracting a positive value k from f(x) shifts the graph of the function downward by k units.

Front

What does f(x - h) represent?

Back

f(x - h) represents a horizontal translation of the graph of f(x) to the right by h units.

Front

What does f(x + h) represent?

Back

f(x + h) represents a horizontal translation of the graph of f(x) to the left by h units.

Front

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

Back

The negative sign reflects the graph of the function over the x-axis.

Front

What does f(-x) represent?

Back

f(-x) represents a reflection of the graph of f(x) over the y-axis.

Front

What is a vertical stretch of 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 is a vertical compression of a function?

Back

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