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Re: A function f(x) is defined for all real numbers as f(x) = (x [#permalink]
2
Carcass wrote:
A function f(x) is defined for all real numbers as f(x) = (x – 1)(x – 2)(x – 3)(x – 4)


Quantity A
Quantity B
f(2.5)
f(3.5)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Quantity A: f(2.5) = (2.5 – 1)(2.5 – 2)(2.5 – 3)(2.5 – 4)
= (1.5)(0.5)(-0.5)(-1.5)
= (POSITIVE)(POSITIVE)(NEGATIVE)(NEGATIVE)
= (POSITIVE)(POSITIVE)(POSITIVE)
= POSITIVE

Quantity B: f(3.5) = (3.5 – 1)(3.5 – 2)(3.5 – 3)(3.5 – 4)
= (2.5)(1.5)(0.5)(-0.5)
= (POSITIVE)(POSITIVE)(POSITIVE)(NEGATIVE)
= (POSITIVE)(NEGATIVE)
= NEGATIVE

Answer: A

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Re: A function f(x) is defined for all real numbers as f(x) = (x [#permalink]
1
Given that f(x) = (x – 1)(x – 2)(x – 3)(x – 4)

Quantity A = f(2.5)

To find f(2.5) we need to substitute x=2.5 in f(x) = (x – 1)(x – 2)(x – 3)(x – 4)
=> f(2.5) = (x – 1)(x – 2)(x – 3)(x – 4) = (2.5 – 1)(2.5 – 2)(2.5 – 3)(2.5 – 4) = 1.5 * 0.5 * -0.5 * -1.5 = 2.25 * 0.25 = 0.5625

Quantity B = f(3.5)

To find f(2.5) we need to substitute x=2.5 in f(x) = (x – 1)(x – 2)(x – 3)(x – 4)
=> f(2.5) = (x – 1)(x – 2)(x – 3)(x – 4) = (3.5 – 1)(3.5 – 2)(3.5 – 3)(3.5 – 4) = 2.5 * 1.5 * 0.5 * -0.5
We can directly stop here as this value is coming negative, but solving to complete the solution
= -0.9375

Clearly Quantity A > Quantity B

So, Answer will be A
Hope it helps!

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