Characters that provide evidence for evolutionary relationships based on shared ancestry are called .

Homologous characters

Explanation:

Homologous character is usually defined as those set of characters that are observed in various organisms and are similar to one another. It is because these organisms have obtained these characters from a common ancestor, having that same distinct characters.

The evolution that occurs in this type of organisms are commonly known as the homologous evolution, where the similarities between the organisms are found in terms of physiology, structure and/or other development, depending upon their common ancestors.

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.