Single Variable Calculus, Chapter 1, 1.4, Section 1.4, Problem 27

a. Graph the functions $y = \sqrt{x}, y = \sqrt[4]{x}$ and $y = \sqrt[6]{x}$ on the same screen using the viewing rectangle of $[-1, 4]$ by $[-1,3]$.







b. Graph the functions $y = x$, $y= \sqrt[3]{x}$ and $y= \sqrt[5]{x}$ on the same screen. Graph the functions $[-3, 3]$ by $[-2, 2]$







c. Graph the functions $y = \sqrt{x}$, $y = \sqrt[3]{x}$, $y = \sqrt[4]{x}$ and $y = \sqrt[5]{x}$ on the same screen. Graph the functions $[-1, 3]$ by $[-1, 2]$







d. State your conclusions from these graphs.

The graphs compresses vertically as the value of the index(exponent at the radical sign) increases. If the index is an even positive integer,
the function is defined only for positive values of $x$. On the other hand, if index is an odd integer, the function is defined for both positive and negative values of $x$.