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

$$f(x)=x$$ $$\text{domain}:(-\infty, \infty)$$ $$\text{range}: (-\infty, \infty)$$ identity function y=x

Squaring Function

$$f(x)=x^2$$ $$\text{domain}:(-\infty, \infty)$$ $$\text{range}: [0, \infty)$$ identity function y=x^2

Cubing Function

$$f(x)=x^3$$ $$\text{domain}:(-\infty, \infty)$$ $$\text{range}: (-\infty, \infty)$$ identity function y=x^3

Square Root Function

$$f(x)=\sqrt{x}$$ $$\text{domain}:[0, \infty)$$ $$\text{range}: [0, \infty)$$ identity function y=sqrt(x)

Cube Root Function

$$f(x)=\sqrt[3]{x}$$ $$\text{domain}:(-\infty, \infty)$$ $$\text{range}: (-\infty, \infty)$$ identity function y=cbrt(x)

Reciprocal Function

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

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