function/graph help

Question

What is the vertex of function f(x)=2|x-1|-3? Does it open up or down? How do you know?

Answer 1

The graph of the absolute value of x-1 is V-shaped, with its lowest point at x=1; ALL other y values are positive.

If you choose to call the lowest point 'vertex' (normally reserved for parabolas), its coordinates are (1,0).  That's why this baby opens upward. The effect of the constant multiplier in front of an absolute value is to double each y value, so the angle in the V gets smaller and its sides are steeper--this is a vertical stretch.

 

THEN when you create f(x) = 2|x-1|-3, all you have to do is to shift every point of the above graph down 3 units.

The range of f(x) is [-3,infinity] and the domain is, of course, all Reals.