Parent Function Transformations

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear functions (y = x), quadratic functions (y = x²), and absolute value functions (y = |x|).

When a function is translated up, the y-values of the function increase by a certain amount. For example, the function y = f(x) becomes y = f(x) + k, where k is a positive number.

When a function is translated down, the y-values of the function decrease by a certain amount. For example, the function y = f(x) becomes y = f(x) - k, where k is a positive number.

When a function is translated left, the x-values of the function decrease by a certain amount. For example, the function y = f(x) becomes y = f(x + k), where k is a positive number.

When a function is translated right, the x-values of the function increase by a certain amount. For example, the function y = f(x) becomes y = f(x - k), where k is a positive number.

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1. For example, the function y = f(x) becomes y = a * f(x), where a > 1.

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1. For example, the function y = f(x) becomes y = a * f(x), where 0 < a < 1.

A horizontal stretch occurs when the input values of a function are multiplied by a factor greater than 1. For example, the function y = f(x) becomes y = f(b * x), where b > 1.

A horizontal compression occurs when the input values of a function are multiplied by a factor between 0 and 1. For example, the function y = f(x) becomes y = f(b * x), where 0 < b < 1.

The absolute value function, y = |x|, reflects all negative y-values to positive, creating a V-shape graph.