SOLUTION: The area of my question is the evaluating of a function. I am at a loss when even beginningto plug in the numbers where they need to go. The problem reads: Given P(x)=4x+7, wr

Algebra ->  Functions -> SOLUTION: The area of my question is the evaluating of a function. I am at a loss when even beginningto plug in the numbers where they need to go. The problem reads: Given P(x)=4x+7, wr      Log On


   



Question 259095: The area of my question is the evaluating of a function.
I am at a loss when even beginningto plug in the numbers where they need to go.
The problem reads: Given P(x)=4x+7, write P(-2+h)-P(-2) in simplest form.
Thanks tons any assistance is greatly appreciated.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Given P(x)=4x+7, write P(-2+h)-P(-2)

Notice that the function letter P always has a parentheses 
( ) right after it.  It starts off with an x in there.

Whatever is in the parentheses ( )after the function letter P is
what you are supposed to substitute in place of the letter x

When you see the definition for P(x), namely this

P(x)=4x+7 

Since there are parenthese around the x after the P,
to see it better, put any x's which are on the right side in 
parentheses too, like this:

P(x)=4(x)+7 

Now empty the x's out those parentheses like this:

P(  )=4(  )+7

That's the way you should think of a function equation. Whatever
anybody puts in the parentheses on the left, that's what you must
put in the parentheses on the right side.

So when you see P(-2+h)  that means to put -2+h in the parentheses
on both the left and right of this

P(  )=4(  )+7

and get

P(-2+h)=4(-2+h)+7

Then you simplify the right side, (but not the left), and get

P(2+h)=-8+4h+7
P(-2+h)=-1+4h


Likewise when you see P(-2)  that means to put -2 in the parentheses
on both the left and right of this

P(  )=4(  )+7

and get

P(-2)=4(-2)+7

Then you simplify the right side, but not the left, and get

P(-2)=-8+7
P(-2)=-1

Therefore when you see

P(-2+h)-P(-2)

since P(-2+h)=-1+4h 

and

since P(-2)=-1

therefore 

P(-2+h)-P(-2) 

means 

(-1+4h)-(-1)

then you simplify that:

P(-2+h)-P(-2) = (-1+4h)-(-1)

P(-2+h)-P(-2) = -1+4h+1

P(-2+h)-P(-2) = 4h

That's all there is to it.  It's so simple it's confusing!

Whatever is in the parentheses after the function letter,
that is what you are supposed to substitute for x in the
original equation for P(x).

Edwin