When a function is shifted, stretched (or compressed), or flipped in any way from its “ parent function “, it is said to be transformed, and is a transformation of a function.

Identify the function family to which f belongs. Compare the graph of f to the graph of its parent function. The graph of f is V-shaped, so f is an absolute value function. The graph is shifted up and is …

We can think graphs of absolute value and quadratic functions as transformations of the parent functions |x| and x². Importantly, we can extend this idea to include transformations of any function …

Parent Function Graphs ... Transformations o all the Parent Functions shown above. Notice the coordinates in Parent Function

A parent function is the simplest form of a family of functions. It’s the most basic, unmodified version of a function type, from which all other functions in that family can be derived through transformations …

We will examine four basic functions and the parent graphs associated with each. This idea can be expanded to many other functions such as cube root, exponential and logarithmic functions.

However, using parent functions and transformation techniques can be an effective way to sketch complicated graphs.