Tom wants to buy a hand held electric drill for woodworking. he wants a light drill this is easy to handle. he also wants a high power drill to be able to easily drill into hardwoods. tom would also like the drill to be cordless, so that he can use it outdoors when necessary. which statement explains why there is NO perfect solution for toms needs

the correct answer should be false

{apex}

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.