Question

How do you graph `f(x) = |x + 3| - 1`?

Answer 1

See graph and explanation.

Explanation:

Consider for a moment `|x+3|`. This produces a graph in the shape of V where the bottom part of the V is on the x-axis

Ok, now look at `|x+3|-1`. The minus 1 lowers the V by 1 below the x-axis.

Now suppose we had just `|x|`. This would produce a V where the y-axis was central. So the left side of the V would be to the left of the y-axis and the right side of the V to the right of the y-axis. Now think about what happens when we change it to `|x+3|`. This moves the whole graph to the left by 3.

So we have: