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, g(x) = f(x) + k shifts the graph up by k units if k > 0 and down if k < 0.

Front

What does a horizontal shift of a function do?

Back

A horizontal shift moves the graph of the function left or right. For example, g(x) = f(x - h) shifts the graph right by h units if h > 0 and left if h < 0.

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. For example, g(x) = -f(x) reflects the graph of f(x) across the x-axis.

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. For example, g(x) = f(-x) reflects the graph of f(x) across the y-axis.

Front

What does a vertical stretch do to a function?

Back

A vertical stretch increases the distance of points on the graph from the x-axis. For example, g(x) = af(x) stretches the graph vertically by a factor of a if a > 1.

Front

What does a vertical compression do to a function?

Back

A vertical compression decreases the distance of points on the graph from the x-axis. For example, g(x) = af(x) compresses the graph vertically by a factor of a if 0 < a < 1.

Front

What does a horizontal stretch do to a function?

Back

A horizontal stretch increases the distance of points on the graph from the y-axis. For example, g(x) = f(bx) stretches the graph horizontally by a factor of 1/b if 0 < b < 1.

Front

What does a horizontal compression do to a function?

Back

A horizontal compression decreases the distance of points on the graph from the y-axis. For example, g(x) = f(bx) compresses the graph horizontally by a factor of 1/b if b > 1.

Front

What is the parent function of a cubic function?

Back

The parent function of a cubic function is f(x) = x^3.