Functions and Graphs

[lizzpalmer]

I have two math problems that I can't seem to solve.

Here's an example of a similar one I think I figured out:

Find: f(6)

f(x) = 3 - 4x
f(6) = 3 - 4(6)
f(6) = 3-24
f(6) = -21

Now for the ones I am having problems with:

The 1st question states:

f(x) = 3 - 4x

a. find f(p) and b. find f(r+1)

for a:

would my answer simply be: f(p) = 3 - 4p

and for b:

would my answer be:

f(r+1) = 3 - 4(r+1)
f(r+1) = 3 - 4r + 4
f(r+1) = 7-4r

It just doesnt seem right.

The second problem that I have is:

f(x) = 8 - x - x2 (the 2 means squared)

if f(p)

so would my answer be:

f(p) = 8 - p - p2 (2 meaning squared)

I couldnt seen to find a way to break it down to something like f(p) = (8 - p)(1+p) so i think I would just leave it as the 8 - p - p2, correct?

 

[lizzpalmer]

The other one I have is very similar to the last one I just posted. f(r+1) = 8 - (r+1) - (r+1)2 (2 being squared)

I couldn't figure a way to break this one down either so I'm assuming it would stay in that form?

 

[mmm4444bot]

would my answer simply be: f(p) = 3 - 4p ? Correct


f(r+1) = 3 - 4(r+1)
f(r+1) = 3 - 4r + 4 ? Arithmetic error when multiplying -4(r + 1)


f(x) = 8 - x - x2 (the 2 means squared)

Type exponents using the caret symbol ^ (shift 6, on most keyboards)

f(x) = 8 - x - x^2


f(p) = 8 - p - p^2 ? Correct

I couldnt [seem] to find a way to [factor the polynomial] … so i think I would just leave it as … 8 - p - p^2, correct?

I would not factor, unless they specifically asked you to report your answer in factored form.

 

[lizzpalmer]

Wow that's great ... Thank you so much!

 

[mmm4444bot]

The other one I have is very similar to the last one I just posted. f(r+1) = 8 - (r+1) - (r+1)^2

A lot of different functions named f are piling up in this thread, but, yes, I think you're correct.


I couldn't figure a way to break this one down either so I'm assuming it would stay in that form?

I would not try to factor it, but you can certainly expand -(r + 1)^2, and then simplify by combining like-terms.

You should get the form f(r + 1) = Ar^2 + Br + C.

 

[lizzpalmer]

Thank you all so much!