I'm about to need tons of help with checking answers. If your willing please help me. There will be lots, this is Algebra I level btw

Question

anonymous · Answer

I can help but I suck at it :)

elise_a18 · Answer

okay thanks at least. I'll tag you in them once i pick out my answers :)

anonymous · Answer

ok hav fun :)

elise_a18 · Answer

recursive function is shown below:

f(1) = 4 and f(n) = f(n - 1) - 8; n > 1

Which of the following lists the terms in the sequence defined by this recursive function?

 4, -4, -12, -20, -28, ...
 4, 4, 12, 20, 28, ...
 4, 12, 20, 28, 36, ...
 4, -12, -20, -28, -36, ...

is it C?

elise_a18 · Answer

@Godlovesme @samanthagreer

anonymous · Answer

I hav 2 go but its c

elise_a18 · Answer

oh kk

elise_a18 · Answer

@AllTehMaffs

anonymous · Answer

So you don't even have to look at any functions other than f(2)!

If we're looking at f(2) (with n=2), what's f(n-1)?

elise_a18 · Answer

f(1)

anonymous · Answer

Yup yup. And we have a definition of f(1).

So if n=2, and if
$$ f(n) = f(n-1) -8$$, 
then we have 
$$f(2) = f(1) - 8$$
and what does that yield?

anonymous · Answer

(it's not C)

elise_a18 · Answer

do it's be f(-7) but none of them start wih that :c

anonymous · Answer

Close!  (and a preemptive apology for the long response) 

So the notation
$$ f(n) $$
doesn't mean the same thing as f*n

It means "f of n."

"f of n" means "what the function is when you plug in n = some number."

For 
$$ f(1)$$ 
the problem says that 
$$f(1) = 4$$
So!  If we're looking at 
$$f(2)$$ 
it means the same thing saying 
$$f(n=2)$$
So you have to plug everything back into the defined function - aka, the defined pattern (recursive functions start with a value then do something to that the make a new pattern).

So! For n=2
$$f(n) = f(n-1)-8$$
means
$$f(2) = f(2-1) - 8$$
$$=f(2) = f(1)-8$$
and we already know that
$$f(1) = 4$$
If you replace 
$$f(1)$$
with
$$4$$
then what does that look like?

elise_a18 · Answer

Oh so it's A?

elise_a18 · Answer

no wait

elise_a18 · Answer

D

elise_a18 · Answer

DX gah i dont know

anonymous · Answer

^_^ Why did you say A the first time?

elise_a18 · Answer

Mm, because it looked right for some reason ;n;

elise_a18 · Answer

>n<

anonymous · Answer

Trust your gut!  

If 
$$f(1) = 4$$
and 
$$f(n) = f(n-1) - 8$$
then
$$f(2) = f(2-1)-8$$
so
$$f(2) = f(1) - 8$$
and what does
$$f(1)=?$$

(it's silly and roundabout, but we're dealing with recursive functions so it's okay ^_~)

elise_a18 · Answer

you gave it to me i think at the top f(1)=4

elise_a18 · Answer

and since it's positive you'd be increasing my 4?

elise_a18 · Answer

-3?

elise_a18 · Answer

i really have no idea how these functions work

elise_a18 · Answer

I've forgotten ;n;

anonymous · Answer

That doesn't mean you're gonna get away with not trying ^_^ And the best part about math is that everything is pretty similar, so even if you've forgotten on part the rest theoretically falls into place if you dwell long enough. 

If
$$f(1) = 4$$
then 
$$f(2) = f(1)-8$$
means
$$f(2) = 4 - 8$$

elise_a18 · Answer

Oh I See it! so you'd just replace f(1) with the equivalent?

anonymous · Answer

Yup yup yup ^_^

elise_a18 · Answer

i son't see how we got f(2) though

anonymous · Answer

It's another "equivalent." if you look at it as
$$y = x-8$$
and 
$$x=4$$
what does that make y?

anonymous · Answer

If
$$f(n) = f(n-1) - 8$$
then we're going to say first that 
$$n=2$$
Then everywhere you see an "n" you replace it with a 2, which gives
$$f(2) = f(2-1)-8$$
Remenber that
$$f(1)=4$$
is a definition for the problem, so everywhere you see the symbol
$$f(1)$$
you can substitute in a 4.  

That gives us
$$f(2) = f(2-1)- 8 \longrightarrow f(2) = f(1) -8 \longrightarrow f(2) = 4-8 \longrightaarow f(2) = -4$$

We can show that the answer is correct by keeping the pattern going.  Just like 
$$f(1) = 4$$
We've shown that
$$f(2) = -4$$
So if we look back at the recursive equation
$$f(n) = f(n-1)-8$$
We're going to say that the next item in the sequence is n=3, giving
$$f(3) = f(3-1) -8$$
so
$$f(3) = f(2)-8$$
and we've shown that 
$$f(2) = -4$$
so 
$$f(3) = (-4)-8$$
meaning
$$f(3) = -12$$
and the first three terms of our recursive function are
$$4, -4, -12, ...$$
which only matches on of the options ^_^

anonymous · Answer

grrrrrr, sorry

the weird typo should say
$$f(2) = f(2-1) - 8 \longrightarrow f(2) = f(1) - 8 \longrightarrow f(2) = 4-8 \longrightarrow f(2) = -4$$

anonymous · Answer

Does that make sense, or is it still a little iffy?

elise_a18 · Answer

Yep I understand it enough to solve other ones. Thanks :)