Transformations of Parent Functions

A parent function is the simplest form of a function in a family of functions, which retains the essential characteristics of that family.

f(x) = √x

The function's output increases by 5 for every input, resulting in a vertical shift upwards.

The graph of y = -|x| is a reflection of y = |x| over the x-axis.

A quadratic function is generally expressed as f(x) = ax² + bx + c, where a, b, and c are constants.

Reflecting a function over the y-axis means that for every point (x, y) on the graph, there is a corresponding point (-x, y).

A negative coefficient in front of a quadratic function causes the graph to open downwards.

f(x) = x³

A quadratic function can be identified by the presence of the x² term and its highest degree being 2.

This equation represents a horizontal translation of the parent function y = x² to the right by 3 units.