Function Transformations

A horizontal shift occurs when the function is translated left or right on the graph. For example, g(x) = f(x - c) shifts the graph of f(x) to the right by c units, while g(x) = f(x + c) shifts it to the left by c units.

This represents a horizontal shift of the function f(x) to the right by 7 units.

A vertical shift occurs when the function is translated up or down on the graph. For example, g(x) = f(x) + c shifts the graph of f(x) up by c units, while g(x) = f(x) - c shifts it down by c units.

This represents a vertical shift of the function f(x) up by 2 units.

A reflection occurs when the graph of a function is flipped over a specific axis. For example, g(x) = -f(x) reflects the graph over the x-axis, while g(x) = f(-x) reflects it over the y-axis.

This represents a reflection over the x-axis, a horizontal shift left by 6 units, and a vertical shift down by 10 units.

A vertical stretch occurs when the graph of a function is stretched away from the x-axis. For example, g(x) = k*f(x) where k > 1 stretches the graph vertically.

This represents a vertical stretch of the function f(x) by a factor of 2.

A horizontal compression occurs when the graph of a function is compressed towards the y-axis. For example, g(x) = f(k*x) where k > 1 compresses the graph horizontally.

This represents a horizontal compression of the function f(x) by a factor of 2.