GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 27 May 2020, 02:22 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Which of the following is the graph of the equation y = |x| for all

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 64152
Which of the following is the graph of the equation y = |x| for all  [#permalink]

### Show Tags

13 00:00

Difficulty:   15% (low)

Question Stats: 69% (00:33) correct 31% (00:43) wrong based on 272 sessions

### HideShow timer Statistics

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 8947 times ]

_________________
Intern  Joined: 25 Nov 2017
Posts: 3
Re: Which of the following is the graph of the equation y = |x| for all  [#permalink]

### Show Tags

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.
CEO  V
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3990
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: Which of the following is the graph of the equation y = |x| for all  [#permalink]

### Show Tags

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...
_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes l Classroom Coaching l On-demand Quant course
Check website for most affordable Quant on-Demand course 2000+ Qns (with Video explanations)
Our SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l
ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3848
Which of the following is the graph of the equation y = |x| for all  [#permalink]

### Show Tags

3
1
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.

_________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date.

Our lives begin to end the day we become silent about things that matter. -- Dr. Martin Luther King, Jr.
Non-Human User Joined: 09 Sep 2013
Posts: 14983
Re: Which of the following is the graph of the equation y = |x| for all  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: Which of the following is the graph of the equation y = |x| for all   [#permalink] 25 Feb 2020, 09:37

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