Parent Functions and Transformations

A parent function is the simplest form of a function type, which serves as a foundation for creating more complex functions through transformations.

The parent function of a quadratic function is $$y = x^2$$ .

The parent function of an absolute value function is $$y = |x|$$ .

Translating a graph to the right means shifting the graph horizontally in the positive x-direction.

Reflecting a graph over the x-axis means flipping the graph upside down, changing the sign of the y-values.

A vertical stretch occurs when the y-values of a function are multiplied by a factor greater than 1, making the graph taller.

The equation is $$y = (x - 2)^2 + 5$$ .

Shifting a graph down means decreasing the y-values by a certain amount, moving the graph lower on the coordinate plane.

A reflection over the x-axis is represented by negating the function, e.g., $$y = -f(x)$$ .

The transformation is a shift right 15 units and down 3 units.