Lesson Objectives
• Learn how to identify the graph of the identity function
• Learn how to identify the graph of the squaring function
• Learn how to identify the graph of the cubing function
• Learn how to identify the graph of the square root function
• Learn how to identify the graph of the cube root function
• Learn how to identify the graph of the reciprocal function

## How to Identify the Graph of a Parent Function

In this lesson, we will show the graphs of six basic functions, which are also known as parent functions. These functions come up often in our study of algebra and math in general. It is a good idea to know the shape, along with the domain and range for these functions.

### Identity Function

$$f(x)=x$$ $$\text{domain}:(-\infty, \infty)$$ $$\text{range}: (-\infty, \infty)$$ ### Squaring Function

$$f(x)=x^2$$ $$\text{domain}:(-\infty, \infty)$$ $$\text{range}: [0, \infty)$$ ### Cubing Function

$$f(x)=x^3$$ $$\text{domain}:(-\infty, \infty)$$ $$\text{range}: (-\infty, \infty)$$ ### Square Root Function

$$f(x)=\sqrt{x}$$ $$\text{domain}:[0, \infty)$$ $$\text{range}: [0, \infty)$$ ### Cube Root Function

$$f(x)=\sqrt{x}$$ $$\text{domain}:(-\infty, \infty)$$ $$\text{range}: (-\infty, \infty)$$ ### Reciprocal Function

$$f(x)=\frac{1}{x}$$ $$\text{domain}:(-\infty, 0) ∪ (0, \infty)$$ $$\text{range}:(-\infty, 0) ∪ (0, \infty)$$ 