horizontal compression and shrink exponenetial functions

In the section, we’ll show you how to identify common parent functions you’ll encounter and learn how to use them to transform and graph these functions. This shows that by learning about the common parent functions, it’s much easier for us to identify and graph functions within the same families. Lastly, when the parent function is reflected over the x-axis and compressed by a scale of 2, it results in the orange graph or y = -2x.The green graph representing y = x- 4 is the result of the parent function’s graph being translated 4 units downward.It’s the result of translating the graph of y =x 4 units upwards. The red graph that represents the function, y =x +4.The rest of the functions are simply the result of transforming the parent function’s graph. Take a look at the graphs of a family of linear functions with y =x as the parent function. This means that the rest of the functions that belong in this family are simply the result of the parent function being transformed.

The parent function of all linear functions is the equation, y = x. The child functions are simply the result of modifying the original mold’s shape but still retaining key characteristics of the parent function.įor example, a family of linear functions will share a common shape and degree: a linear graph with an equation of y = mx+ b. To understand parent functions, think of them as the basic mold of a family of functions. As a refresher, a family of functions is simply the set of functions that are defined by the same degree, shape, and form. In short, it shows the simplest form of a function without any transformations. Parent functions are the fundamental forms of different families of functions.

You’ll also learn how to transform these parent functions and see how this method makes it easier for you to graph more complex forms of these functions. Refresh on the properties and behavior of these eight functions. In this article, learn about the eight common parent functions you’ll encounter. Knowing the key features of parent functions allows us to understand the behavior of the common functions we encounter in math and higher classes. These graphs are extremely helpful when we want to graph more complex functions. Parent functions represent the simplest forms of different families of functions.

Horizontal compression and shrink exponenetial functions