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

Question

Which of the following is the graph of the equation y = |x| for all real values of x? (Note: All graphs drawn to scale.) https://gmatclub.com/forum/download/file.php?id=39229 2017-12-17_1244.png

banuprakash · Answer

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

Answer: B

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GMATinsight · Answer

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

Answer: Option B

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...
ANswer:m . option B

generis · Answer

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.

Answer B

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 ).

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.

Answer B

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

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

Prep Toolkit

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