# How do you graph and find the vertex for #abs y = abs(x-3)#?

There are ways of achieving this analytically, but the simplest method is to generate a few sample data pairs:

# (x,y):#

#(-1,+-4) #

#(0,+-3) #

#(1,+-2)#

#(2+-1)#

(#3,0)#

I will assume by "vertex" you mean the point where the two lines cross;

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To graph and find the vertex for ( |y| = |x - 3| ):

- Recognize that the equation represents the absolute value function.
- Plot the vertex, which is at the point (3, 0).
- Draw the V-shape graph of the absolute value function centered at the vertex (3, 0).
- Since the absolute value function is symmetric about its vertex, you can mirror the V-shape across the y-axis to complete the graph.

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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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