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 c – c = 0. 

Note:  You do not know whether a or b is equal to c, so you cannot assume that a – c or b – c 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

The correct answer is (C).

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

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