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`

1 Answer

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embizze | High School Teacher | (Level 2) Educator Emeritus

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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.


The answer is (c)