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

1 Answer
Mar 12, 2016

See graph and 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:
Tony B