How do you graph and find the vertex for $| y | = x$ $abs y=x$ ?

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Answer 1 · 2015-05-26T21:30:09

The vertex of a function containing a modulus is typically at the point where the enclosed expression changes sign.

In the case of $| y | = x$ $abs(y) = x$ the vertex is at $(0, 0)$ $(0,0)$

When $y \geq 0$ $y >= 0$ the equation boils down to $y = x$ $y = x$ - the equation of a $45^{o}$ $45^o$ line with slope $1$ $1$ .

When $y < 0$ $y < 0$ the equation boils down to $- y = x$ $-y = x$ , that is $y = - x$ $y = -x$ - the equation of a line with slope $- 1$ $-1$ .

graph{x=abs(y) [-10, 10, -5, 5]}

How do you graph and find the vertex for |y|=xabs y=x?