Question

the graph of a function is shown below. which family could this function belong to?
https://flic.kr/p/2ov2d6k
select one:
a. exponential
b. logarithmic
c. square root
d. cube root

Explanation:

• Exponential functions have a horizontal asymptote and are always positive for base >1, which does not match the graph crossing the origin and having negative x-values with negative outputs.
• Logarithmic functions are only defined for positive x-values, but the graph has points for negative x, so this is not a match.
• Square root functions are only defined for non-negative x-values, which does not fit the graph's negative x-domain.
• Cube root functions ($f(x)=\sqrt[3]{x}$ or transformed versions) are defined for all real x, pass through the origin, and have a curve that increases slowly, matching the given graph's shape and behavior.

Answer:

d. Cube Root