answer-
the statement that f(x) = |x+a| + b has exactly one x-intercept is sometimes correct.
solution-
it solely depends on b, whether the function will have one or two or zero x intercept.
this plot of the given function, f(x) = |x+a| + b will be the basic absolute value graph i.e v shape, with vertex translated to (-a, b), instead of origin.
1- if b is zero, the graph will have exactly one x-intercept, at x= -a
2- if b is positive, the whole graph will be above the x-axis, hence it will have no x-intercepts.
3- if b is negative, the graph will be below the x-axis, hence it will have two x-intercepts.
β΄ the statement is sometimes true.