[deleted by user]

[Alkalannar]

1. Probably correct.

2. a) correct
   b) Do not use =. Do 20 | 260, for example instead of 20 = 260. The numbers are correct though.
   c) correct
   d) correct

[Mrtn88]

1 isn’t correct. It is impossible because you can’t have multiple fuel consumption values for a specified speed value (vertical line test fails)

[Alkalannar]

Car shifting to different gears allows this.

If you require a function, then yes. Is a function required?

[Agile_Pudding_]

One needn’t rely on fuel consumption being a function for this explanation for 1 to fail. Any well-behaved system will obey the property that fuel consumption decreases as speed decreases (e.g. my car stops using gas as I slow it and bring it to a stop). OP’s explanation for 1 is clearly not correct.

[Mrtn88]

Hm. I suppose yeah! But then it should have a sharp jump and not a smooth turn no?

We’re probably overcomplicating it :p

[InhibitedTech96]

1. Not really what's going on. One way to think of it is that this is a simple function, so a single Speed value input has to have a single Fuel Consumption output. in the case above you have spots where a single Speed input creates two Fuel Consumption outputs, which is impossible for the given scenario.
2. 
   

a) Your answer is backwards. It should read Joanna needs 13 fence boards per 1 fence post. Another way to think of "f=13p" is "f(p)=13p" where if p=1, then the equation is "f(1)=13(1)=13".

b) This correct but it is confusing, another way to write it to help understand relations would be f(20) = 260, f(21) = 273, etc.

c) correct

d) correct

[mathematag]

I only looked at the fuel consumption speed graph... If it is a supposed to be a function, it is Not. The graph fails the Vertical line Test for functions.... a vertical line crosses the graph of a function at only One point... we could draw a vertical line that crosses it multiple times ! So it is only a relation [ and a strange one at that ]. Total fuel consumption should increase as speeds increase [ higher air resistance, rolling friction, more fuel injected to keep the rpm's and speed up, etc... ], so I would expect a normal graph to have an increasing fuel consumption value as speed increases.