What is this equation? What does the 1 stand for. Is the amount for the server supposed to be the total or the tip. No context from other questions. Please help!

This an optional brain teaser my math teacher does and most of them I've figured out but this one is stumping me

I am so stuck, i've tried my best, and havent been able to get into my teacher to ask, help will be appreciated

How do I solve this? Like, what steps do I take? The decimal points are confusing me a bit.

Is there anyway to do this without using derivative?

for clarity’s sake, f’(x) isn’t the function drawn onto the graph, it’s the one that’s printed. the drawn function was my answer to 8e.

it might be hard to tell, but the f’(x) graph hits the x-axis just past where 3 is. I was a little unsure while taking the test what to put, but then I realized that the function looked like a wave, and I realized it was probably pi.

according to her, this was wrong. there’s apparently no one answer: I could’ve said 3, or 3.1, or something. but the problem was that apparently pi is not on the number line, and that it’s too much effort for her to figure out that pi/2 is a little more than 1.5. even though I marked on the graph with the inflection points where it was.

(in case you’re wondering, e WAS meant to be f(x). she made a mistake and told us to scribble out “the inverse” and replace it with “f(x)“. I got 8e right.)

am I wrong, or is this completely absurd?? I guess that maybe pi is a bit of a stretch to come to if that wasn’t the intent, but if that were the case I should’ve gotten one point off at the start and the rest should‘ve been fine for self-consistency. but apparently I was “treating it like radians” so I got a point off for each one.

Is this right? Or should these all add up to 30 as per the question? Thanks

Tbh i dont get anything he says about logs. I haven't done like one question successfully. Today he got mad that my hw clearly "wasnt attempted" even though i took like an hour trying to do it. If i dont get these right he'll skin me but nobody in my life is a higher maths student and they all just go wtf is that. My dad definitely doesnt know it either, but he'll act like he does and then yell the wrong thing at me for an hour. Genuinely what the fuck is going on i haven't understood a word out of him the past 2 classes and neither does the girl next to me.

Tried asking the class nerd and he just clowned on me

Not drawn to scale ofc, sorry

i was thinking that i´d add the 2x+1 to make it 3x/3=-1 but im unsure on how it would even continue.

Hey so this might seem like a silly question but I want to know if you have a -x = 4 if it turns into a -4. I have the other parts of the graphing completed it’s just this part that I don’t want to make a mistake on!!! Thank you in advance

P.S- the reason it’s says elementary/highschool math is because I am taking a beginner math class not a algebra class In elementary

I’m struggling to define whether it’s B or E. Both are imperfect answers in my opinion. If I chose B, then the upward position would be repeated, and if I chose E then the sequence of additional lines is odd (although it could make sense in terms of completeness: i.e. one line, two lines, three lines, zero lines)
What do people think?
In my opinion the right answer would be a downward arrow with four lines

Edit/Update:

After reading so many different opinions, I feel these kind of questions only make sense if teachers are testing a reasoning process and not just “the right answer”. As a matter of fact, the right answer is supposed to be B, we later learned. It was frustrating because the p-set had at least 5 questions that followed the exact same pattern (it was just a rose with leaves, or a zebra with stripes, etc instead), and of course kids were graded bad without building or promoting any reasoning skills.

Just started my freshman year and learned my math teacher doesn't allow retrys on homework so im trying to get comfortable with this work quickly. I am somewhat familiar with the basics from last year but complex shapes like these confuse me.

How do I solve these? I know how to solve a system of equations normally but my head is blank when it comes to these questions, we didn’t do this type of question in class.

I did a bit of reading into this, this is a Grandi's series iirc?, and aren't both options b and c correct here? as both are valid approaches to the problem? the correct answer is 1/2 as per the solution set.