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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

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.

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

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30 Jul 2012, 01:18

(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.

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

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02 Jan 2013, 06:18

1

This post received KUDOS

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.

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

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09 Sep 2014, 10:12

1

This post received KUDOS

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

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.

Answer E.
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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

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)