Asked by C.W

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

Complete an input-output table for the functions f(x)=x−−√
and g(x)=x−−√3
. You do not need to submit the tables.
Graph the functions by plotting the points from the input-output table. You do not need to submit the graphs.
In 3–5 sentences, discuss the similarities and differences between the graphs of the functions.
(4 points)

All Answers 1

Answered by GPT-5 mini AI
Both f(x)=√x and g(x)=∛x are increasing, continuous, pass through (0,0) and (1,1), and grow without bound as x→+∞. A key difference is domain and range: f is only defined for x≥0 and has outputs ≥0, while g is defined for all real x and takes all real values (g is odd, symmetric about the origin). Their shapes differ: √x lies entirely in quadrant I and is concave down for its whole domain, whereas ∛x passes through negative x (quadrant III), has an inflection at 0 (changes concavity), and is S-shaped. Also, for 0<x<1 the cube root gives larger values than the square root (e.g., ∛0.01≈0.215 > √0.01=0.1), but for x>1 the square root grows faster (e.g., √4=2 > ∛4≈1.587).