Determine whether each equation has a graph that is symmetric wit...

Question

Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. 
|y| = -x

Accepted Answer

Identify if the graph defined by the following equation is symmetric with respect to the origin X axis Y axis or nut where we have the absolute value of 11 Y is equal to X. Let's take the x axis symmetry 1st. For the X axis, we want to see if we replace Ry with a negative way. Do we get the same answer back out? Let's take a look. The absolute value of 11 times negative way. Ethical sex or native Lebanon Y is equal sex. Now with absolute values, if we have the absolute value of a negative number, that is the same thing as saying the absolute value of that number is positive. So here we can say this turns back into absolute value 11 Y&C equal to X. Yeah, the same thing as our original. So we can say this is symmetrical across the X axis. Let's take the Y axis. Now, y axis, we're gonna replace our X with a negative X. So we'll say absolute value of 11 Y is equal to negative x. No, this is actually not the same as our original. So this does not pass the check. So it is not symmetrical on the Y axis. For the origin. We want to see if both are true. At the same time, they're both symmetrical across the X axis and the Y axis by replacing Y and X. So Y all turn to native Y X will turn into native X, We will get absolute value 11 times negative way is equal to negative X or as if I have negative 11, Y is equal to negative X 11 Y is equal to negative x. This has not passed the check, which means we're only symmetrical across the X axis, which means our answer to our problem is the answer. Hey, okay, I hope to help you solve the problem. Thank you for watching. Goodbye.

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Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. |y| = -x