Question

2. What is the vertex of the function g(x) = |x - 3| - 1? (A) (B) (c (3,1) (3,1) (-3,-1 (-3,1)

Answer 1

Consider first the graph of the function |x|. It looks like this

for this graph, the vertex is located at (0,0). Now, the function |x-3| has the same graph as |x| but shifted 3 units to the right. It looks like this

In this case, the vertex is located at (3,0). Finally, for the function |x-3|-1 we shift the graph of |x-3| one unit down. So we get

This means that the vertex of this graph is (3,-1).