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# Which of the following is the graph of the equation y = |x| for all

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Posts: 53063
Which of the following is the graph of the equation y = |x| for all  [#permalink]

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17 Dec 2017, 00:48
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Difficulty:

5% (low)

Question Stats:

73% (00:32) correct 27% (00:38) wrong based on 217 sessions

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Which of the following is the graph of the equation y = |x| for all real values of x? (Note: All graphs drawn to scale.)

Attachment:

2017-12-17_1244.png [ 18.49 KiB | Viewed 6619 times ]

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Re: Which of the following is the graph of the equation y = |x| for all  [#permalink]

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Updated on: 17 Dec 2017, 05:29
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
(−∞,∞)

For each
x value, there is one y value.

Try x= 1,0,-1 then
Y=1,0,1

So if you plot

Graph looks like a V Shape

Sent from my ZUK Z2132 using GMAT Club Forum mobile app

Originally posted by banuprakash on 17 Dec 2017, 02:50.
Last edited by banuprakash on 17 Dec 2017, 05:29, edited 1 time in total.
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Re: Which of the following is the graph of the equation y = |x| for all  [#permalink]

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17 Dec 2017, 04:50
Bunuel wrote:
Which of the following is the graph of the equation y = |x| for all real values of x? (Note: All graphs drawn to scale.)

Attachment:
2017-12-17_1244.png

Draw the graph of the line Y=X which will be a positive sloping line passing therough origin making 45º with positive X-Axis

Flip the figure of line available below the X-axis towards upside (i.e. convert all negative values of Y into positive values of Y

We get a V shape figure

ALTERNATIVELY

Keep substituting value of x and calculate values of Y and polot all the avialble points to get the graph

@x = 0, y = 0
@x = 1, y = 1
@x = 2, y = 2
@x = -1, y = +1
@x = -2, y = +2
and so on...
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Which of the following is the graph of the equation y = |x| for all  [#permalink]

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17 Dec 2017, 13:09
3
Bunuel wrote:
Which of the following is the graph of the equation y = |x| for all real values of x? (Note: All graphs drawn to scale.)

Attachment:
2017-12-17_1244.png

This question can be solved in 10 seconds if this property is known:

V-shaped graph

The graph of a linear absolute value function is V-shaped.

The V-shape can be upright, upside down, or sideways.

There is only one V-shaped graph in this group.

Plot points in two phases ("pieces")

If the V-shape is not at your fingertips, then you can plot points, but how absolute value behaves changes "regular" linear graphing.

Linear absolute value functions are written in two pieces, where y = f(x):

$$f(x) = x$$, for $$x\geq{0}$$

$$f(x) = -x$$, for $$x < 0$$

The first part means you must plot some x-values that are 0 and positive.

The second part means you must choose some x-values that are negative ($$x < 0$$).
[(0,0) can be included with negative x, where (-0 = 0), but that is a long story.]

A note of caution: it might seem perfectly reasonable to plot
$$y = -x$$, so one point is $$(5, -5)$$

That is arithmetically true, but
It is not consistent with the absolute value function where
-- the variable inside (here, $$x$$), must be considered in both +/- cases (absolute value function makes a negative value positive or non-negative).

Plot three points for both cases

1) $$y = f(x) = x$$

$$(0,0), (1, 1), (2, 2)$$

2) $$y = f(x) = -x$$: choose points that make the value inside the brackets negative (i.e. $$f(x)$$ where $$x < 0$$)

$$(0,0), (-1, 1), (-2,2)$$

Now there are two straight lines in a V-shape.

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Re: Which of the following is the graph of the equation y = |x| for all  [#permalink]

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13 Jan 2019, 16:26
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Re: Which of the following is the graph of the equation y = |x| for all   [#permalink] 13 Jan 2019, 16:26
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