Using translation concepts, it is found that the rule for g(x) and it's graph is given by:
[tex]g(x) = x^3 + 4[/tex]
What is a translation?
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we have that:
[tex]f(x) = x^3 - 10[/tex]
Applying the rule for g(x), we have that:
[tex]g(x) = f(x) + 14[/tex]
[tex]g(x) = x^3 - 10 + 14[/tex]
[tex]g(x) = x^3 + 4[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
