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# On the graph above, when x = 1/2, y = 2; and when x = 1, y =

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Math Expert
Joined: 02 Sep 2009
Posts: 44298
On the graph above, when x = 1/2, y = 2; and when x = 1, y = [#permalink]

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30 Jul 2012, 01:53
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On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

Practice Questions
Question: 7
Page: 153
Difficulty: 600

[Reveal] Spoiler:
Attachment:

Graph.png [ 6.01 KiB | Viewed 31377 times ]
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44298
Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y = [#permalink]

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30 Jul 2012, 01:54
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SOLUTION

On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

Since the graph is symmetric with respect to line $$x = 2$$, then the value of $$y$$ when $$x = 3$$ will be the same as the value of $$y$$ when $$x = 1$$, so 1.

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Intern
Joined: 27 Jul 2012
Posts: 25
Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y = [#permalink]

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30 Jul 2012, 02:18
(E) 1

its symmetric with respect to x=2.
when x=1, 1 unit to the left of x(2), y is 1.
when x=3, 1 unit to the right of x(2), y should again be 1 as it is symmetric.
Senior Manager
Joined: 13 Aug 2012
Posts: 453
Concentration: Marketing, Finance
GPA: 3.23
Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y = [#permalink]

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02 Jan 2013, 07:18
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Bunuel wrote:
Attachment:
Graph.png

On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

Half of the entire graph is a mirror image of the other side. The center coordinate is (2,0) according to the graph. Thus, y when x=1 and y when x-3 are equal.

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Impossible is nothing to God.

Manager
Joined: 07 Apr 2014
Posts: 130
Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y = [#permalink]

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09 Sep 2014, 11:12
1
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Bunuel wrote:
Attachment:
Graph.png
On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

Practice Questions
Question: 7
Page: 153
Difficulty: 600

graph is symmetric with respect to the vertical line

so if x = 1, y = 1 & x=2 , y=0 then x=3 , y=1 ...
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2116
Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y = [#permalink]

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19 May 2016, 10:24
4
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Expert's post
Bunuel wrote:
Attachment:
Graph.png
On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

We are given that the graph is SYMMETRIC along the vertical line x = 2. We are also given that when x = 1, y = 1. We are asked to determine the value of y when x is 3. Keep in mind that when x = 1, it is ONE UNIT away from the line x = 2, and when x = 3, it is also ONE UNIT away from the line x = 2.

Since the y-coordinate is 1, when x is 1, the y-coordinate is ALSO 1 when x is 3. Again, this is because the graph is symmetric with the line x = 2.

Another way to look at this problem is to see that the point (1,1) is actually being reflected over the line x = 2.

We see that the point (1,1) is exactly 1 unit from the line x = 2. In fact the point (2,1) is on the line x = 2 which is exactly 1 unit from (1,1). However, (1,1) is exactly 1 unit on the LEFT of (2,1), so by symmetry, the point that is exactly 1 unit on the RIGHT of (2,1) is (3,1). Thus the y-coordinate is 1.

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Jeffery Miller

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Joined: 12 Sep 2015
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Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y = [#permalink]

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07 Oct 2017, 14:10
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Bunuel wrote:

On the graph above, when x = 1/2, y = 2; and when x = 1, y = 1. The graph is symmetric with respect to the vertical line at x = 2. According to the graph, when x = 3, y =

(A) -1
(B) -1/2
(C) 0
(D) 1/2
(E) 1

We're told that the graph of the parabola is symmetric with respect to the vertical line at x = 2
So, for example, notice that the point (0,3) lies on the parabola.
This point is 2 units to the LEFT of the line of symmetry.

This means that there's also a point that is 2 units to the RIGHT of the line of symmetry.
So, the coordinates of that point are (4,3)

Likewise, we're told that the point (1,1) lies on the parabola.
This point is 1 unit to the LEFT of the line of symmetry.

This means that there's also a point that is 1 unit to the RIGHT of the line of symmetry.
So, the coordinates of that point are (3,1)

[Reveal] Spoiler:
E

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Re: On the graph above, when x = 1/2, y = 2; and when x = 1, y =   [#permalink] 07 Oct 2017, 14:10
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