Comparing the Graphs of Power Functions Graph the

Chapter 2, Problem 2.1.1.170

(choose chapter or problem)

Comparing the Graphs of Power Functions Graph the functions in the stated windows and explain how the graphs are alike and how they are different. Consider the relevant aspects of analysis from Example 2. Which ordered pairs do all four graphs have in common?

(a) \(f(x)=x^{-1},\ g(x)=x^{-2},\ h(x)=x^{-3}\text{, and }k(x)=x^{-4}\text{ in }\text{ the windows }[0,\ 1]\text{ by }[0,\ 5],[0,\ 3]\text{ by }[0,\ 3]\text{, and }[-2,\ 2]\text{ by }[-2,\ 2].\)

(b) \(f(x)=x^{1/2},\ g(x)=x^{1/3},\ h(x)=x^{1/4},\text{ and }k(x)=x^{1/5}\text{ in }\text{ the windows }[0,\ 1]\text{ by }[0,\ 1],\ [0,\ 3]\text{ by }[0,\ 2]\text{, and }[-3,\ 3]\text{ by }[-2,\ 2].\)