Which of the following may be correctly expressed by the gra

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Tue Feb 05, 2019 1:07 pm

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GMATH practice exercise (Quant Class 4)

Which of the following may be correctly expressed by the graph representation given above?

(A) y = |x|^2
(B) y = 2^x
(C) y = x^(-1/2)
(D) y = x^(-1)
(E) y = x^(-2)

Answer: [spoiler]_____(E)__[/spoiler]

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

Source: Beat The GMAT — Problem Solving | Tue Feb 05, 2019 1:07 pm

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Wed Feb 06, 2019 4:47 am

fskilnik@GMATH wrote:

GMATH practice exercise (Quant Class 4)

Which of the following may be correctly expressed by the graph representation given above?

(A) y = |x|^2
(B) y = 2^x
(C) y = x^(-1/2)
(D) y = x^(-1)
(E) y = x^(-2)

FOCUS: graph association

From the figure given:

> We expect y to decrease whenever |x| increases, in other words, whenever x > 0 gets larger or x < 0 gets smaller (i.e., more negative).
> This is enough to refute (A) and (B).

> We expect y to be defined for all values of x, except when x is zero.
> This is enough to refute (C): when x < 0, x^(-1/2) is not defined.

> We expect y to be positive for all nonzero values of x.
> This is enough to refute (D): when x<0, x^(-1) is negative.

The correct answer is therefore (E), by exclusion!

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

P.S.: more quantitative mature students may also take into account the symmetry related to the y-axis, in the sense that we expect f(x) = f(-x) ...

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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