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Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

If the function function f is defined by function f of x = (x minus a) times (x minus b) over (x minus c), where 0 less than a less than b less than c, for which of the following values of x is function f undefined?

roman numeral 1 a

roman numeral 2 b

roman numeral 3 c

 

Answer Choices

Correct!

Explanation

If x = a, then (x minus a) times (x minus b) over (x minus c) = (a minus a) times (a minus b) over (a minus c) = 0 over (a minus c) = 0. If x = b, then (x minus a) times (x minus b) over (x minus c) = (b minus a) times (b minus b) over (b minus c) = 0 over (b minus c) = 0. If x = c, then (x minus a) times (x minus b) over (x minus c) = (c minus a) times (c minus b) over (c minus c) = (c minus a) times (c minus b) over 0, which is not defined because division by 0 is undefined. Therefore, of the three values, a, b, and c, the only one for which function f is undefined is c. Thus the correct response is roman numeral 3 only.

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