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

Answer 1

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

In the case of #abs(y) = x# the vertex is at #(0,0)#
When #y >= 0# the equation boils down to #y = x# - the equation of a #45^o# line with slope #1#.
When #y < 0# the equation boils down to #-y = x#, that is #y = -x# - the equation of a line with slope #-1#.

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

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Answer 2

To graph ( y = |x| ), plot points for ( y ) based on the absolute value of ( x ). The vertex of the absolute value function ( y = |x| ) is at the origin (0, 0). Therefore, the vertex for the function is (0, 0).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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