# Functions

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## 4/30 Functions

Always try to solve the problem as if the answer choices weren't there. This has two benefits: it makes you more efficient at multiple-choice questions, and it makes you more confident on grid-in questions. First, read carefully and look for important information. Identify the bottom line, then assess your options and select the most efficient way to solve the problem. Attack the problem, solve it quickly, and loop back to ensure that the answer you found matches the bottom line. Finally, check the answer choices and select the correct answer.

If the function f is defined by $f(x)=\frac{(x-a)(x-b)}{(x-c)}$, where 0 < a < b < c, for which of the following values of x is f undefined?

I. a
II. b
III. c

Read carefully and focus on the bottom line.

f undefined when x = ?

The most important clue here is the word "undefined." What does "undefined" mean in a math problem? It means that you have attempted to do something impossible, such as dividing by zero. In order for this function to divide by zero, x - c must equal zero because it is the denominator. Given that, there is only one possible value for x. Any number minus itself equals zero, so if x = c, then x - c = 0. Any other answer choice would yield a positive or negative number for the denominator, and the function would not be undefined. Only choice III makes the function undefined.

Now look at the answer choices:

A) None

B) I only

C) III only

D) I and II only

E) I, II, and III