# Q. If x is real, the expression `[(x-a)(x-b)]/(x-c)` will assume all real values if A) `a>b>c` B) `a<b<c` C) `a>c>b` D) `b>a>c`

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Expert Answers

embizze | Certified Educator

Assumes all values means that the **range** is all real numbers.

Takes all values means the domain is all real numbers. The domain is restricted in all of the cases as x cannot equal c.

You can use guess and check to get an answer: try the numbers 1,2, and 3 for a,b,c.

(a) a=3,b=2,c=1 The function `y=((x-3)(x-2))/(x-1)` :

does not take on all values.

(b) a=1,b=2,c=3 the function `y=((x-1)(x-2))/(x-3)` :

does not take on all values.

(d) b=3,a=2,c=1 is the same as (a)

(c) a=3,c=2,b=1 the function `y=((x-3)(x-1))/(x-2)` :

clearly takes on all values.

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The answer is (c)

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