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 vertical shift of a function do?

Back

A vertical shift moves the graph of the function up or down. For example, f(x) + k shifts the graph up by k units, while f(x) - k shifts it down by k units.

Front

What is a horizontal shift of a function?

Back

A horizontal shift moves the graph of the function left or right. For example, f(x - h) shifts the graph right by h units, while f(x + h) shifts it left by h units.

Front

What is a reflection in the x-axis?

Back

A reflection in the x-axis flips the graph of the function over the x-axis. This is represented by -f(x).

Front

What is a reflection in the y-axis?

Back

A reflection in the y-axis flips the graph of the function over the y-axis. This is represented by f(-x).

Front

What does a vertical stretch do to a function?

Back

A vertical stretch increases the distance of the graph from the x-axis. For example, k*f(x) stretches the graph vertically by a factor of k if k > 1.

Front

What does a vertical compression do to a function?

Back

A vertical compression decreases the distance of the graph from the x-axis. For example, k*f(x) compresses the graph vertically by a factor of k if 0 < k < 1.

Front

What does a horizontal stretch do to a function?

Back

A horizontal stretch increases the distance of the graph from the y-axis. For example, f(k*x) stretches the graph horizontally by a factor of 1/k if k > 1.

Front

What does a horizontal compression do to a function?

Back

A horizontal compression decreases the distance of the graph from the y-axis. For example, f(k*x) compresses the graph horizontally by a factor of 1/k if 0 < k < 1.

Front

How do you identify a reflection in the x-axis from a function's equation?

Back

If the function's equation includes a negative sign in front of the function, such as g(x) = -f(x), it indicates a reflection in the x-axis.