Question

My teacher keeps adamantly telling me that the answer is D, and I insist it’s B. Am I right or is she right?

My reasoning, question asks for an ALWAYS true statement. Question gives 6 defined points that if plotted will show it will need to cross the x axis twice to connect all the points while being continuous. Yet functions aren’t always straight and simple so two is the bare mininum and there may be more as in between those defined points the line may have crossed multiple times. However D and C assume its exactly 2 or more than 2, therefore they are wrong. If D and C merged together then that would be better than B. Yet B is still correct on the terms of being an “always” correct statement.

Answer 1

the picture below is more or less some quick mockup of what that might be, and yes, 2 solutions or zeros is the bare minimum, because we know only 5 points on this continuous line, but it could have jumped a few times before going forwards and we are not privy to those points.

well, we can say that

f(x) has more than one zero

f(x) has exactly two zeros

I think within the circumstance both are acceptable, exactly 2 zeros is also acceptable, but is not exclusively the only valid choice, if any we could say "exactly 2 zeros" is a subset of the superset "more than one zero".

kinda like saying Sandra has Felines and she also has 3 cats, well, 3 cats are an exact number, but the plural Felines contains them, so both statements are equally valid, one is more general than the other, is all