# Functions

## Algebra: Functions

Read the following SAT test question and then select the correct answer.

Always use the same process for math problems on the SAT.  Read carefully and make a note of the bottom line.  Then assess your options and choose the most efficient method to attack the problem.  When you have an answer, loop back to be sure it matches your bottom line.

If the function f is defined by , where 0 < a < b < c, for which of the following values of x is f undefined?

I. a
II. b
III. c

Bottom Line: For which value(s) of x is f undefined?

Assess your Options: You could pick numbers, but that will get confusing with three variables.  You could just start plugging in the variables a, b, and c for x and then simplify the function, but you will end up wasting time.  Time is precious on the SAT!  Start with the information that you are given and think about it logically.

Attack the Problem:  Always think about the information that you are given before you jump into the problem.  The inequality that you are given simply tells you that all of your variables are positive numbers.  A function or a fraction is undefined whenever it is divided by zero because you cannot divide by zero.

Think about it logically:  do you care what is on the top of the fraction?  No!  Focus on the bottom of the fraction.  How can you make x c = 0?  The variable that you are changing in this problem is x.  If you set x = to c, then cc = 0.

Note:  You do not know whether a or b is equal to c, so you cannot assume that ac or bc would equal 0.  If you plug those variables in, you still have a lot of variables on the bottom!

Loop Back:  You found the only answer that will work out of the three that you were given.  Look down at your answer choices.

(A) None
(B) I only
(C) III only
(D) I and II only
(E) I, II, and III

On sat.collegeboard.org, 53% of the responses were correct.

For more help with SAT math, visit www.myknowsys.com!

# 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