Compare the square root and cube root functions by completing the following: A) Complete an input-output table for the functions f(x)=x−−√ and g(x)=x−−√3 . You do not need to submit the tables. B) Graph the functions by plotting the points from the input-output table. You do not need to submit the graphs. C) In 3–5 sentences, discuss the similarities and differences between the graphs of the functions.
A) The input-output table for the function f(x)=√x would have values such as x: 0, 1, 4, 9 and corresponding y = f(x) values as 0, 1, 2, 3.
The input-output table for the function g(x)=∛x would have values such as x: 0, 1, 8, 27 and corresponding y = g(x) values as 0, 1, 2, 3.
B) The graphs of the square root function (√x) and the cube root function (∛x) would both start at the point (0,0). However, the square root function would increase gradually and then steepen, while the cube root function would increase slowly and then steepen even more than the square root function.
C) The graphs of the square root function and the cube root function are similar in that they both start at the point (0,0) and increase as x increases. However, the square root function increases faster than the cube root function. Additionally, the square root function is defined for negative x-values, while the cube root function is defined for all real numbers. These differences result in the square root function having a steeper curve compared to the cube root function.