What does the graph of |y|=|x| look like? I can only find that y=|x| looks like a V...?

Question

Please provide an explanation, thanks!

Answer 1

Its a big X with the center at the origin..



think of it as y = x and y = -x.



The simplest explanation is because all of the values in these two graphs satisfy |y| =|x|.



another way is think of the V of y =|x| and flip it, you have two V's meeting at their point, looking like an X.



think of the absolute value as flipping parts of the graph around.



A first guess that many people have is that the answer is

y = x only on the 1st quadrant.



This is wrong since The point (-1, -1) satisfies |y| = |x|.



In mathematics, a counterexample is wnough to disprove a notion btw. And I'm sorry for bashing any other answers that come up.

Answer 2

for

|y|=|x|

notice that y and x can take all the values both + and -

because of the modulus sign(only + values are filtered out).

this is not the case in y=|x| where y can only take positive values.

hence the solutions are y=x and y=-x.

and the graph looks like a V in the first 2 quadrants and an inverted v in the 3rd and the fourth quadrant

or a X

Answer 3

The graph will be two straight lines inclined at 45° and 135° to the x-axis passing through the origin.

For example

When x= -2

|y|=|x|=|- 2 |= 2 i.e y = -2 and -y =2 i.e. y=2

Hence for every value of 'x' there are two values of 'y'

Answer 4

a graph of absolute values of y and x is only in the first quadrant.



Since all values of x and y are positive, then they are located on the first quadrant of a cartesian plane. Hence, it's right portion of a V. something like this : '' / ''

Answer 5

When yo go from y = x to y = mod(x) you flip any negative y values to positive ones to get a V shape.



To go from y = mod(x) to mod(y) = mod(x) you do the same again for any negative x values. You are left with the section of the original line y=x that exists ONLY in the top right quadrant.

Answer 6

well, you know y=|x| is a V. It'll be a cross for |x|=|y|, the point of intersection being the origin.

Or in other words, you'll have another V upside down in addition to the V in y=|x|.

Answer 7

graph it on a graphics calc

Answer 8

median of the first quarter.