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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) (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
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