The graphs of the square root function \( f(x) = \sqrt{x} \) and the cube root function \( g(x) = \sqrt[3]{x} \) have some interesting similarities and differences. Both functions pass through the origin (0,0), meaning they both output zero when the input is zero. However, the square root function only exists for non-negative inputs (x ≥ 0) and increases slowly, while the cube root function exists for all real numbers (positive and negative) and increases at a steeper rate, crossing the x-axis at different points.
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)=3^√x−− . 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 sentences, discuss the similarities and differences between the graphs of the functions. Like a 9th grader.
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