Parent functions are the simplest form of a family of functions. Knowing these "parents" helps you quickly understand how transformations (shifts, stretches, and reflections) affect a graph. Think of them as your building blocks for understanding more complex functions!
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Linear Function | A. A function of the form $f(x) = x^2$ |
| 2. Quadratic Function | B. A function of the form $f(x) = |x|$ |
| 3. Absolute Value Function | C. A function of the form $f(x) = x$ |
| 4. Square Root Function | D. A function of the form $f(x) = \sqrt{x}$ |
| 5. Cubic Function | E. A function of the form $f(x) = x^3$ |
Complete the following paragraph using the words: transformation, parent function, origin, reflection, stretch.
The simplest function in a family of functions is called the __________. Understanding the __________ helps you predict how a graph will change. A __________ can shift a graph away from the __________ or flip it over an axis. A __________ makes the graph wider or narrower.
Explain, in your own words, how the graph of $f(x) = (x-2)^2 + 3$ is related to the graph of its parent function. What transformations have occurred?
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