in a population of fruit flies grown in laboratory conditions, a new phenotype arises. instead of the typical red eyes, a purple-eyed individual is seen. This individual survives to adulthood and is able to mate with other flies. two students studying the fruit fly population discuss the origin of the purple-eyed fruit fly. one student insists that the fly came from outside of the original fruit fly population. the other student claims that the fly originated from within the laboratory fruit fly population. which statements defend the claim of student two that the new phenotype originated from within the fruit fly population?

idk im sorry.

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.