To shift the function [tex]\(f(x) = x^2 + 5x - 6\)[/tex] 4 units to the left, we replace [tex]\(x\)[/tex] with [tex]\(x + 4\)[/tex] in the function.
The new function [tex]\(g(x)\)[/tex] is obtained by substituting [tex]\(x + 4\)[/tex] into [tex]\(f(x)\)[/tex]:
[tex]\[ g(x) = f(x + 4) \][/tex]
Let's perform this substitution step-by-step:
1. Replace every [tex]\(x\)[/tex] in [tex]\(f(x)\)[/tex] with [tex]\(x + 4\)[/tex]:
[tex]\[ f(x + 4) = (x + 4)^2 + 5(x + 4) - 6 \][/tex]
Thus, the function [tex]\(g(x)\)[/tex] is:
[tex]\[ g(x) = (x + 4)^2 + 5(x + 4) - 6 \][/tex]
This matches option B:
[tex]\[ g(x) = (x + 4)^2 + 5(x + 4) - 6 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
