SAT Prep of the Day 2

Word of the Day:
INTERIM --- done, made, appointed, or occurring for an intervening time.
"The team named Bill Thomas as their interim coach after their head coach got fired last week."

Question of the Day:
If the function ƒ is defined by ƒ(x) = [(x-a)(x-b)] / (x-c) , where 0 < a < b < c. For which of the following values of x is ƒ undefined?

1. a
2. b
3. c

a) None
b) I only
c) III only
d) I and II only
e) I, II, III

You have to start the question by knowing what they are asking. Here they want you to determine values for which the function is
undefined. When is a function undefined? In a rational function (a function with one polynomial over another), when the denominator
cannot be equal to 0. Therefore, the function is undefined for any x values that make the denominator equal to 0.

This question is a little bit tougher because instead of using numbers, it uses letters to represent numbers. Remember though that a, b,
and c are just representing some number so don't be fooled! They are NOT variables or anything else complicated. So in this function,
the only term in the denominator is (x-c). That term will be equal to 0 when x = c. Therefore, only option III is true and that corresponds
to answer choice C.

When x = a or x = b, the function will simply be equal to 0 because you will have 0 in the numerator. At those values, the function is
still defined!!!