check answer please... given the function f described by f(x)=-x-4....find f(-8)

Question

anonymous · Answer

2?

e.mccormick · Answer

Not 2.  That would be f(-6)

anonymous · Answer

oh wait i multiplied

rajee_sam · Answer

y = -x-8; put x = -8 for f(-8); y = - ( -8) - 4; y = 8-4 = 4

anonymous · Answer

i did it all wrong then. wait if i use -6 it would be 4?

rajee_sam · Answer

f(-6) will be y= - (-6)-4 = 6-4 = 2

e.mccormick · Answer

The key here is watching the signs.  $f(-8)=-(-8)-4$  Beacuse the x is replaced with the $-8$ the sign goes along.  Then the $-(-8)$ can be said to be  $(-1)\times (-8)$ which is just 8.

anonymous · Answer

dont i substitute -8 for -x?

e.mccormick · Answer

Not for -x, but for x.

anonymous · Answer

ok so i would have -8=-x-4?

e.mccormick · Answer

No, that is replacing f(x) with -8.  That is the wrong place to replace it.  f(x) means, "The function f with respect to the variable x."

anonymous · Answer

ok im a little confused

e.mccormick · Answer

Lets take it one part at a time.  First, the function name.  If it is $f(x), g(x), h(a)$ or whatever, that part just tells you the name of the function and what variable you are dealing with.  This time it is the function $f$ and the variable $x$.

e.mccormick · Answer

That is all the left hand side of this means.  With me so far?

anonymous · Answer

ok got it.

e.mccormick · Answer

The right hand side is what equation the function represents.  This time it happens to be $-x-4$.  It can be one of many, many equations, but at the moment it is just that one.

anonymous · Answer

so i have to work from the -x-4

e.mccormick · Answer

Yes.  What $f(-8)$ means when you have $f(x)=-x-4$ is this.  "Look at $-x-4$ and any time you see $x$, replace it with $(-8)$.  And I mean including the ( ) to help make it clear.

anonymous · Answer

oh hold on let me see if i have it..

anonymous · Answer

so if i replace it, it would be -8=-x-4

e.mccormick · Answer

Still replacing the wrong part.  You write it out like this: $f(-8)=-(-8)-4$

anonymous · Answer

ohh duhhh. see i was thinking not -x cause of it being negative duhhh

e.mccormick · Answer

Hehe.  Well, it is still an x.  And there is even a 1 hiding there.  It can be said that $-x-4=-1x-4$

anonymous · Answer

ok so it would be -8=-(-8)-4? do i still put the negative sign with the 8 because theres one already there?

e.mccormick · Answer

Yes, even though there already is one, you need to bring along the entire $-8$.  Now, what happens to a $-$ when two negative numbers are multiplied?

e.mccormick · Answer

You keep premoving the f on the left.  The f stays there.  You can change it to y, but that is it!  So iy would be 
$f(-8)=-(-8)-4$ or $y=-(-8)-4$

anonymous · Answer

it would be a postitive

anonymous · Answer

so i would get 32

e.mccormick · Answer

Yes!  So:
$f(-8)=-(-8)-4$ means:
$f(-8)=-1\times (-8)-4$ which simplifies to:
$f(-8)=8-4$

The -8 becomes positive.  Do you get that part now?

e.mccormick · Answer

Umm, still did a multiplication rather than a subtraction...  not 32.

anonymous · Answer

it would be a -4,, if subtraction -8 and 4

e.mccormick · Answer

The -4 means subtract 4.  That - sign stays there.

anonymous · Answer

what i keep thinking of changing the subtraction sign to a plus and the 4 become -4..is that something of what your saying?

e.mccormick · Answer

It has always been a -4.
 $f(x)=-x\Large-4$ $\leftarrow$ there it is, a -4.

anonymous · Answer

ok i was getting off on something else

e.mccormick · Answer

No problem.  You are obviously just starting functions.  It is a new topuc.  New topics tend to be confusing.

anonymous · Answer

yea i just started them. the function machines i can do a little better with, but this problem i just dont get lol

e.mccormick · Answer

So now, if we leave the $f(-8)$ alone, and remember that the $(-8)$ replaces every x, negative or not, and that $-4$ stays negative because it does not have an x with it to cause any changes, we gt this far:

$f(-8)=-(-8)-4\implies $
$f(-8)=-1\times (-8)-4\implies $
$f(-8)=8-4$

What is the last step?

anonymous · Answer

I think i subtract and get 4 lol

e.mccormick · Answer

/cheer
Yes

anonymous · Answer

im really smart i am lol

e.mccormick · Answer

Hey!  Don't knock yourself.  Like I said, this is all new.  You are learning a language.  It is the language of math.  Before you know the rules, how can you use them to say the right things mathematically?

anonymous · Answer

so my answer would be 4? ive always struggled in math. made good grades in math but it was always hard for me to understand. i need to read more on it lol

e.mccormick · Answer

Yes, the answer is 4.

And don't knock yourself.  Like I said, this is all new.  You are learning a language.  It is the language of math.  Before you know the rules, how can you use them to say the right things mathematically?

Like $\implies$.  Did you know that is a word in math?  It means "implies" and $\therefore$ means therefore.  Until you knew what $+$, $-$, $\times$, and $\div$ meant, you could not use them properly!

anonymous · Answer

yea seems like the more higher in math you go the higher the language goes too lol thanks for your help!

anonymous · Answer

im just checking my work to see if i have them all correct.

e.mccormick · Answer

So the new term you are learning is "function" and it comes with a whole new set of rules to follow.  There are restrictions, like the vertical line test, and eventually you will learn what a one-to-one function is.  Along the way, you will have to use what you already know and you will have to fit it all in together.

e.mccormick · Answer

This keeps changing too.  Knwo how $\cdot$ is used to mean $\times$?  I am in lineear al;gebra, and at that point $\cdot$ means dot product and $\times$ means cross product and they are different!  So yah, as you keep going it changes.

Speaking of linear, I have to go to class!  Hehe.  Have fun here!

anonymous · Answer

lol have a great time!