SAT Subject Test Mathematics Level 2

The issue of “defined” and “undefined” functions is brought up by Example 5. This question is
typical of what you might encounter on the Math 2 test.

Example 5

UNDEFINED

To  find    values  of  x   for which   a   function    is  undefined,  look    for values  that    would   make    a

denominator zero    or  that    would   make    an  expression  under   a   radical negative.

There are two things to watch out for when looking for values for which a function is undefined.
First, watch out for division by zero. And second, watch out for negatives under radicals. In this case
you have both.

The function is undefined when the denominator is zero:

1. If    ,  what    are all the values  of  x   for which   f(x)    is  defined?

(A) All real    numbers except  4

(B) All real    numbers except  −2  and 2

(C) All real    numbers greater than    or  equal   to  −2  and less    than    or  equal   to  2

(D) All real    numbers less    than    or  equal   to  −2  or  greater than    or  equal   to  2

(E) All real    numbers less    than    or  equal   to  −2  or  greater than    or  equal   to  2,  except  4