Question

If f(x) = 2 for all real numbers x, then f(x+2) =
(A) 0
(B) 2
(C) 4
(D) x
(E) The value cannot be determined.

Answer 1

Say we have an equation f(x)=x^2 f(2) will equal 4 while f(x+2)=4^2 or 16
Now say f(x)=x+800, f(2)=802 f(x+2)=804
problem is f(x)=2 doesn't tell us a function involving x, so how can we possibly determine f(x+2)?

Answer 2

f(x) as a function could be anything as long as f(x)=2

Answer 3

The answer is B, but I perplexed as to how to get the answer.
I understand that when f(x) is plugged it, 2 is yielded.

Does that mean that the answer remains the same for any function?

Answer 4

But it says f(x)=2 for all real numbers x

Answer 5

This book has very poor explanations, idk :O

Answer 6

So f(4)=2, f(anything)=2 agreed?

Answer 7

any real number so f(x+1000) must equal?

Answer 8

2?

Answer 9

Yes

Answer 10

Is there a specific rule or no?

Answer 11

So if for all real numbers f(x)=2
f(x+2) where x is a real number will be no different

Answer 12

@Zarkon do you know how to solve this? I'm still very confused

Answer 13

plug in 2 into x

Answer 14

@Albert0898 are you with me

Answer 15

"If f(x) = 2 for all real numbers x"

the f(5)=2
f(y)=2
f(456436346346x+3453535)=2

whatever you plug in you get 2

Answer 16

f(x)=2 has a graph that is a horizontal line with height 2

Answer 17

if x is a real number then x+2 is a real number


therefore f(x+2)=...

Answer 18

then the answer is 4

Answer 19

f(x+2) must have an x value among all real numbers
f(x) must have an x value among all real numbers (-inf,inf)
So f(x)=2
Now say x=2
what will f(2) be equal to?

Answer 20

That won't change if x=4 right?

Answer 21

That won't change if f(x)=f(x+500)
no matter the input x the output is 2

Answer 22

I think I get it now!
f(x) = y = 2
f(x+2) is equal to y which is equal to 2?

@DannyO19
@Zarkon
@Daniel56k

Answer 23

yeah the first sentence in the prob says it is same y for all x, horizontal line Y=2

f(x - a) is a way to take the whole graph of the function, and shift it horizontal 'a' units.

Answer 24

so after applying f(x+2) the thing shifts left 2 units this time, (a=-2)

this prob is just y = constant value so really it doesnt matter, but that is that

Answer 25

Oh I get it now! Thanks!

Answer 26

like say you choose x=2, the function will give you f(4), that is 2 units pelletf left...