It is currently 09 Jul 2020, 21:46

### 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

# The figure above shows the graph of the function f defined

Author Message
TAGS:
Director
Joined: 16 May 2014
Posts: 597
GRE 1: Q165 V161
Followers: 112

Kudos [?]: 621 [0], given: 64

The figure above shows the graph of the function f defined [#permalink]  29 May 2014, 02:05
Expert's post
00:00

Question Stats:

60% (01:04) correct 39% (01:28) wrong based on 23 sessions
Attachment:

axis.jpg [ 15.18 KiB | Viewed 9428 times ]

The figure above shows the graph of the function $$f$$ defined by $$f(x) = |2x|+ 4$$ for all numbers $$x$$. For which of the following functions $$g$$, defined for all numbers $$x$$, does the graph of g intersect the graph of $$f$$ ?

(A) $$g(x) = x - 2$$

(B) $$g(x) = x + 3$$

(C) $$g(x) = 2x- 2$$

(D) $$g(x) = 2x+ 3$$

(E) $$g(x) = 3x - 2$$
[Reveal] Spoiler: OA

_________________

My GRE Resources
Free GRE resources | GRE Prep Club Quant Tests
If you find this post helpful, please press the kudos button to let me know !

Last edited by Carcass on 29 Nov 2017, 12:12, edited 2 times in total.
Edited the question and added the OA
Director
Joined: 16 May 2014
Posts: 597
GRE 1: Q165 V161
Followers: 112

Kudos [?]: 621 [0], given: 64

Re: Practice Question #3 [#permalink]  29 May 2014, 02:07
Expert's post

Explanation

You can see that all five choices are linear functions whose graphs are lines with various slopes and y-intercepts. The graph of Choice A is a line with slope 1 and y-intercept shown in the following figure
Attachment:

3s.JPG [ 13.56 KiB | Viewed 10473 times ]

It is clear that this line will not intersect the graph of f to the left of the y-axis. To the right of the y-axis, the graph of f is a line with slope 2, which is greater than slope 1. Consequently, as the value of x increases, the value of y increases faster for f than for g, and therefore the graphs do not intersect to the right of the y-axis. Choice B is similarly ruled out. Note that if the y-intercept of either of the lines in choices A and B were greater than or equal to 4 instead of less than 4, they would intersect the graph of f.

Choices C and D are lines with slope 2 and y-intercepts less than 4. Hence, they are parallel to the graph of f (to the right of the y-axis) and therefore will not intersect it. Any line with a slope greater than 2 and a y-intercept less than 4, like the line in Choice E, will intersect the graph of f (to the right of the y-axis). The correct answer is Choice E.
_________________

My GRE Resources
Free GRE resources | GRE Prep Club Quant Tests
If you find this post helpful, please press the kudos button to let me know !

Director
Joined: 09 Nov 2018
Posts: 505
Followers: 0

Kudos [?]: 54 [0], given: 1

Re: Practice Question #3 [#permalink]  05 Jan 2019, 05:59
soumya1989 wrote:

Explanation

You can see that all five choices are linear functions whose graphs are lines with various slopes and y-intercepts. The graph of Choice A is a line with slope 1 and y-intercept shown in the following figure
Attachment:
3s.JPG

It is clear that this line will not intersect the graph of f to the left of the y-axis. To the right of the y-axis, the graph of f is a line with slope 2, which is greater than slope 1. Consequently, as the value of x increases, the value of y increases faster for f than for g, and therefore the graphs do not intersect to the right of the y-axis. Choice B is similarly ruled out. Note that if the y-intercept of either of the lines in choices A and B were greater than or equal to 4 instead of less than 4, they would intersect the graph of f.

Choices C and D are lines with slope 2 and y-intercepts less than 4. Hence, they are parallel to the graph of f (to the right of the y-axis) and therefore will not intersect it. Any line with a slope greater than 2 and a y-intercept less than 4, like the line in Choice E, will intersect the graph of f (to the right of the y-axis). The correct answer is Choice E.

it is a original explanation from ETS.
Anybody please make it more clear.
Manager
Joined: 01 Nov 2018
Posts: 87
Followers: 0

Kudos [?]: 62 [1] , given: 22

Re: The figure above shows the graph of the function f defined [#permalink]  12 Feb 2019, 21:12
1
KUDOS
Expert's post

The function is |2x|+4
all the answer choices have a positive slope.
automatically, we disregard the negative half of the absolute value function and only focus on the positive side of f(x) meaning we will not accept any x value less than 0 as an answer for the intersection, giving us the equation 2x+4

now that we are only dealing with the positive sloped part of the absolute value function, take a look at each of the answer choices.
x-2 will never be greater than 2x+4 if X is positive.
try it.
x-2=2x+4
-6=x, this will be the case for any choices that have either a smaller slope, and/or a smaller intercept.
choice E has a larger slope, so lets give that a try.

3x-2=2x+4
x=6
boom, it works.

Choose E
GRE Instructor
Joined: 10 Apr 2015
Posts: 3532
Followers: 133

Kudos [?]: 3995 [0], given: 65

Re: The figure above shows the graph of the function f defined [#permalink]  24 May 2019, 15:48
Expert's post
soumya1989 wrote:
Attachment:
axis.jpg

The figure above shows the graph of the function $$f$$ defined by $$f(x) = |2x|+ 4$$ for all numbers $$x$$. For which of the following functions $$g$$, defined for all numbers $$x$$, does the graph of g intersect the graph of $$f$$ ?

(A) $$g(x) = x - 2$$

(B) $$g(x) = x + 3$$

(C) $$g(x) = 2x- 2$$

(D) $$g(x) = 2x+ 3$$

(E) $$g(x) = 3x - 2$$

--------------------------
ASIDE: Some students may be unfamiliar with the above format.
The most common way to define a line or curve is to write y = some expression involving x (e.g., y = 2x - 5)
Just know that graphing the equation y = 2x - 5, is the same as graphing the function f(x) = 2x - 5

Likewise, graphing the function f(x) = |2x|+ 4 is the SAME as graphing the equation y = |2x|+ 4
--------------------------

Let's first find the slope of one of the arms of the graph.

To do so, let's find 2 points that lie on the graph.

f(0) = |2(0)|+ 4
= |0|+ 4
= 4
So, when x = 0, y = 4
(0, 4) is one point.

f(1) = |2(1)|+ 4
= |2|+ 4
= 6
So, when x = 1, y = 6
(1, 6) is another point.

Apply the slope formula to get: slope = (6 - 4)/(1-0) = 2/1 = 2
So, the slope of the red arm is 2

At this point, we might see that the graphs for answer choices C and D both have slope 2.
We know this because each is written in slope y-intercept form

For example, g(x) = 2x - 2 (aka y = 2x - 2) represents a line with slope 2 and a y-intercept of -2
Likewise, g(x) = 2x + 3 represents a line with slope 2 and a y-intercept of 3

Since both lines have the same slope of the red arm of our graph, they are PARALLEL with the red arm.
This means neither line will ever intersect the graph of f

ELIMINATE C and D

Now notice that the graphs for answer choices A and B both have slope 1.
That is, g(x) = x - 2 (aka y = 1x - 2) represents a line with slope 1 and a y-intercept of -2
And g(x) = x + 3 represents a line with slope 1 and a y-intercept of 3
Since both lines have a slope that's LESS THAN 2, both lines will diverge away from the red arm.
So, neither line will ever intersect the graph of f

ELIMINATE A and B

By the process of elimination, the correct answer is E, but let's check it out for "fun"
The graph for answer choice E (y = 3x - 2) has slope 3.
Since the slope of y = 3x - 2 is steeper than the red arm of the graph, we know that the lines will intersect at some point.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: The figure above shows the graph of the function f defined   [#permalink] 24 May 2019, 15:48
Display posts from previous: Sort by