1. Hypothesize in what type of environments it would be advantageous for a protist to be autotrophic, heterotrophic, or mixotrophic.

See below

Explanation:

Protists fall into the category of eukaryotes. They are diverse in nature and typically are found to be single celled organisms containing very organized structures.They are classified based on what is their source of nutrition.

Autotrophic - capable of photosynthesis to produce their own food, so an environment where sunlight, CO2 and water is available.

Heterotrophic - feed on other organisms , an environment where prey is plenty and very limited or no access to sunlight.

Mixotrophic - a combination of the above two, an environment with all of the aforementioned factors present.

the areas around the equator

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.