Marvin blows up a balloon but lets go of it. the air inside is released and the balloon goes up into the air. what best describes what happens? a) gravity pushes the balloon into the air. b) drag is caused by contact of the balloon with the air. c) lift lowers the air pressure on the top of the balloon. d) the thrust of the air propels the balloon in the opposite direction.

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.

∴ the statement is sometimes true.