In the digestive system, peristalsis is: a) a common cause of loss of appetite, fatigue, and dehydration. b) a process of fat emulsification in the small intestine. c) voluntary control of the rectal sphincters regulating defecation. d) the transport of nutrients to the liver through the hepatic portal vein. e) smooth muscle contractions that move food along the esophagus.

Option E, Smooth muscle contractions that move food along the esophagus.

Explanation:

Peristalsis is an involuntary movement of muscles (smooth and longitudinal) in the digestive tract to move the food from Oseophagus to other hollow tubes and stomach.

These Peristaltic waves  are strong wave like smooth muscle movement in the esophagus, stomach, and intestines as the bolus of food is swallowed to process food in different digestive tract.

Hence, option E is correct

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.