As you have probably already studied, the equation is the equation for a circle, with center at the origin (figure below).
The following is a visual investigation of the graphs , for a circle, n = 2. Let's take a look at the graphs of when n > 2. We will pay close attention to the graphs when n is odd and when n is even.
Let's let n = 3, 5, and 7. These graphs are shown below. Compare these graphs with that of the circle. What is different? What is similar? Describe the domain and range.
Now let n = 4, 6, and 8. Compare the graphs below with that of the circle. How have the graphs changed? Note the difference and similarities to that of the circle. Describe the domain and range.
Make a conjecture about the graphs of , for n > 2, if n is odd and if n is even.
How do you think the graphs of n = 24 and n = 25 will look? Once you have made an educated guess, check the graphs to see if you are correct.