Which cranial nerve innervates several different systems including blood pressure, digestion, and cardiac rhythm?

Vagus nerve.

Explanation:

Vagus nerve is the tenth cranial nerve and largest among all the cranial nerves. This nerve transmits information to or from the surface of brain to the tissue or organ.

Vagus nerve is responsible for regulation of various functions like sweating, blood pressure, digestion, peristalsis and cardiac rhythmicity. Cranial nerve innervates in different system of body like digestion, blood pressure and cardiac rhythm.  

answer-

the statement that f(x) = |x+a| + b has exactly one x-intercept is sometimes correct.

solution-

it solely depends on b, whether the function will have one or two or zero x intercept.

this plot of the given function, f(x) = |x+a| + b will be the basic absolute value graph i.e v shape, with vertex translated to (-a, b), instead of origin.

1-   if b is zero, the graph will have exactly one x-intercept, at x= -a

2- if b is positive, the whole graph will be above the x-axis, hence it will have no x-intercepts.

3- if b is negative, the graph will be below the x-axis, hence it will have two x-intercepts.

∴ the statement is sometimes true.