Common Algebra Mistakes
Function Notation 
Some problems provide the opportunity for more than one mistake. The Goal
Evaluate f(x+h) for the function: The Mistakes
Find the mistakes:
(Roll the mouse over the math to see a hint in red) (Roll the mouse over the math to see a hint in red) A Correct Solution
(Roll the mouse over the area above to see the corrections in blue) Explanations
In the first mistake f(x+h) is computed to be f(x)+h. There are very few functions f(x) for which the equation f(x+h) = f(x) + h is true (it is true if y = f(x) is a straight line with slope 1). In the second example the +h is again in the wrong place.
Follow the sequence of examples:
Whatever we replace x with replaces x in the formula (even something silly like #):
Replace x with 0.5 to find f(0.5):
Note that 0.5 can be written as 0.4+0.1:
Following the pattern we can find f(0.4+h):
And f(x+h) is a matter of replacing the 0.4 by x:

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