Compare the square root and cube root functions by completing the following:

Question

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.

Answer 1

C) Both the square root and cube root functions have a similar shape with a curved, increasing trend. However, the cube root function has a steeper curve compared to the square root function. The cube root function increases more rapidly as the input values increase, while the square root function has a slower rate of increase. Additionally, the square root function has a domain of all real numbers greater than or equal to zero, while the cube root function has a domain of all real numbers.