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A function f(x) is defined for all real numbers by the expre
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14 May 2019, 01:08
14 May 2019, 01:08
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85% (01:04) correct
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A function f(x) is defined for all real numbers by the expression (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5). For which one of the following values of x, represented on the number line, is f(x) negative?
(A) Point A
(B) Point B
(C) Point C
(D) Point D
(E) Point E
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Re: A function f(x) is defined for all real numbers by the expre
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14 May 2019, 13:56
14 May 2019, 13:56
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Expert Reply
Recognize that for any product to be negative there must be an odd number of negative multiplicands. Check the choices to see which results in an odd number of negative values.
For Choice A: All four values are < 0 --> Negative x Negative x Negative x Negative will result in a product > 0 | Eliminate Choice A
For Choice B: x - 1.5 is the only value > 0 --> Positive x Negative x Negative x Negative will result in a product < 0 | Select Choice B
Since one choice works, you can stop testing at this point.
For Choice A: All four values are < 0 --> Negative x Negative x Negative x Negative will result in a product > 0 | Eliminate Choice A
For Choice B: x - 1.5 is the only value > 0 --> Positive x Negative x Negative x Negative will result in a product < 0 | Select Choice B
Since one choice works, you can stop testing at this point.
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Re: A function f(x) is defined for all real numbers by the expre
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15 Dec 2021, 10:22
15 Dec 2021, 10:22
2
Given that f(x) = (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5) and we need to find which of the answer choice is negative
A. f(1)
To find f(1) we need to substitute x=1 in f(x) = (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5)
=> f(0.5) = (1 – 1.5)(1 – 2.5)(1 – 3.5)(1 – 4.5) = NEGATIVE * NEGATIVE * NEGATIVE * NEGATIVE = POSITIVE * POSITIVE = POSITIVE
B. f(2)
=> f(2) = (2 – 1.5)(2 – 2.5)(2 – 3.5)(2 – 4.5) = POSITIVE * NEGATIVE * NEGATIVE * NEGATIVE = NEGATIVE * POSITIVE = NEGATIVE
We don't need to proceed further as we already got the answer. But solving remaining options to complete the solution
C. f(3)
=> f(3) = (3 – 1.5)(3 – 2.5)(3 – 3.5)(3 – 4.5) = POSITIVE * POSITIVE * NEGATIVE * NEGATIVE = POSITIVE * POSITIVE = POSITIVE
D. f(4.5)
=> f(4.5) = (4.5 – 1.5)(4.5 – 2.5)(4.5 – 3.5)(4.5 – 4.5) = POSITIVE * POSITIVE * POSITIVE * ZERO = ZERO = Neither POSITIVE Nor NEGITIVE
E. f(5.5)
=> f(5.5) = (5.5 – 1.5)(5.5 – 2.5)(5.5 – 3.5)(5.5 – 4.5) = POSITIVE * POSITIVE * POSITIVE * POSITIVE = POSITIVE * POSITIVE = POSITIVE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
A. f(1)
To find f(1) we need to substitute x=1 in f(x) = (x – 1.5)(x – 2.5)(x – 3.5)(x – 4.5)
=> f(0.5) = (1 – 1.5)(1 – 2.5)(1 – 3.5)(1 – 4.5) = NEGATIVE * NEGATIVE * NEGATIVE * NEGATIVE = POSITIVE * POSITIVE = POSITIVE
B. f(2)
=> f(2) = (2 – 1.5)(2 – 2.5)(2 – 3.5)(2 – 4.5) = POSITIVE * NEGATIVE * NEGATIVE * NEGATIVE = NEGATIVE * POSITIVE = NEGATIVE
We don't need to proceed further as we already got the answer. But solving remaining options to complete the solution
C. f(3)
=> f(3) = (3 – 1.5)(3 – 2.5)(3 – 3.5)(3 – 4.5) = POSITIVE * POSITIVE * NEGATIVE * NEGATIVE = POSITIVE * POSITIVE = POSITIVE
D. f(4.5)
=> f(4.5) = (4.5 – 1.5)(4.5 – 2.5)(4.5 – 3.5)(4.5 – 4.5) = POSITIVE * POSITIVE * POSITIVE * ZERO = ZERO = Neither POSITIVE Nor NEGITIVE
E. f(5.5)
=> f(5.5) = (5.5 – 1.5)(5.5 – 2.5)(5.5 – 3.5)(5.5 – 4.5) = POSITIVE * POSITIVE * POSITIVE * POSITIVE = POSITIVE * POSITIVE = POSITIVE
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Functions and Custom Characters
