An absolute value function of the form f(x)=|x+a|+b has exactly one x-intercept

absolute-value

#1

An absolute value function of the form f(x)=|x+a|+b has exactly one x-intercept

Answer:

It depends on what b is.

This graph is the basic absolute value graph (V shape, with vertex at the origin) translated until its vertex is at (-a, b).

So if b is positive, the whole graph will be above the x-axis and will have no x-intercepts.

If b is zero, the graph will have exactly one x-intercept.

If b is negative, the graph will have two x-intercepts.