SOLUTION: <pre> For the given function, find f(x+h)-f(x) 覧覧覧覧覧 h f(x) = xｲ - 8x A) 2x - 8 + h B) 2xh+h2-8h-16w/h C) 2x + h D) 2x + 8 + h My

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Question 458813: 
For the given function, find 

f(x+h)-f(x) 
覧覧覧覧覧 
     h

f(x) = xｲ - 8x 
 
A) 2x -  8 + h 
 
B) 2xh+h2-8h-16w/h
  
C) 2x + h 
 
D) 2x +  8 + h 
 
My brain doesn't even know where to begin on this one.. 
tho for some reason my brain thinks the answer is b.. 
but doesn't know how?

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
For the given function, find 

f(x+h) - f(x)
覧覧覧覧覧覧
      h


f(x) =  xｲ - 8x 
 
===================================================

To find

f(x+h) - f(x)
覧覧覧覧覧覧
      h

1.  First find f(x+h)

f(x) =  xｲ - 8x

That is, replace every x by (x+h), and get

f(x+h) = (x+h)ｲ - 8(x+h)

Now simplify the right side:

f(x+h) = (x+h)(x+h) - 8x - 8h
f(x+h) = xｲ + hx + hx + hｲ - 8x - 8h
f(x+h) = xｲ + 2hx + hｲ - 8x - 8h

2. Now substitute xｲ + 2hx + hｲ - 8x - 8h for f(x+h) in

f(x+h) - f(x)
覧覧覧覧覧覧  
      h

and get

xｲ + 2hx + hｲ - 8x - 8h - f(x)
覧覧覧覧覧覧覧覧覧覧覧覧覧覧
              h

3. Now substitute (xｲ - 8x) for f(x) in that:

xｲ + 2hx + hｲ - 8x - 8h - (xｲ - 8x)
覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧
                h

Remove the parentheses in the numerator:

xｲ + 2hx + hｲ - 8x - 8h - xｲ + 8x
覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧
               h

Now the xｲ and the -xｲ cancel, and 
the -8x and the +8x cancel, giving:

2hx + hｲ - 8h
覧覧覧覧覧覧
      h

4. Now factor out h in the numerator:

h(2x + h - 8)
覧覧覧覧覧覧
      h

5. Now cancel the h factor in the numerator and
the denominator and get:

2x + h - 8

Now if you will swap the last two terms you will
get choice A). 

A) 2x - 8 + h 
 
Edwin
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