Question

If f(c) = 0, which of the following statements must be true?
(Points : 2)
x + c is a factor of f(x).

The point (0,c) lies on the graph of f(x).

x - c divides evenly into f(x).

The point (-c,0) does not lie on the graph of f(x).

Answer 1

understand that f(c) = 0 is another way of indicating y=0

Answer 2

hmm .... it cannot be x+c because the format is x-c
the point 0,c makes sense
x-c divides evenly also makes sense

so would it be one of the middle two?

Answer 3

is y dependent or independent?

Answer 4

independent

Answer 5

y is always dependent… it is dependent on the values of x or functions associated with x

Answer 6

opps... okay

Answer 7

let me try to give you some examples of what I mean
let us say I have a f(x) = 2x^2
as I have said before, it is another way of indicating y = 2x^2
so when we evaluate f(-2) it will be y = 2(-2)^2
now the value of y rest solely on the values of x or functions associated with x
it will be y = 2*4
y = 8
or f(-2) = 8

Answer 8

then it would be -c,0 does not lie on the graph?

Answer 9

let me try another function
say: g(x) = 1/x
and we were to evaluate g(4) and then g(f(x))
first we do this,
g(4) = 1/x
g(4) = 1/4
or simply y = 1/4

now let us evaluate g(f(x))
first we obtain f(x) from our previous example
f(x) = 2x^2
then evaluate g(f(x))
it will be g(f(x)) 1/(2x^2)
since our f(x) is now the x in the g(x)

Answer 10

in your question, we are clearly missing some information based on the options of answers provided. perhaps your question is relevant to another set of question(s) or previous question.

if not, then every time we see f(x) = 0
it must clearly state that y = 0
the format maybe tricky for starters, but it is simply telling you f(x) = 0*x
and no matter what we do, it will always come back as zero.

Answer 11

are you following me?

Answer 12

not really... i got lost with your last post

Answer 13

did you follow before the last post?

Answer 14

yes

Answer 15

okay, good

Answer 16

what does f(c) = 0 mean then?

Answer 17

um if im correct i think its x-c divides evenly into f(c)

right?

Answer 18

*f(x)

Answer 19

where are you getting the x?

Answer 20

the independent variable?

Answer 21

but c is our independent variable in f(c) = 0
you can replace x with anything in a function it is just a place holder for any independent variable
f(monkey) = 0 is just another way of saying f(monkey) = zero times monkey

Answer 22

mkay

Answer 23

that is why I said earlier that you might be missing some information or have forgotten to include something else that makes x okay to exist

Answer 24

ohh okay!! :) thank you!

Answer 25

there is no x in f(c) = 0