Approximately 10% of people living in the United States are allergic to penicillin. A research team has developed a new antibiotic that could potentially replace penicillin and treat a wide variety of bacterial infections. To test their theory, the scientists grow Streptococcus pyogenes in petri dishes. S. pyogenes causes numerous infections in humans, like pharyngitis, tonsillitis, and scarlet fever. These diseases are normally treated successfully with penicillin. They expose S. pyogenes to their new strain of antibiotic to determine its effectiveness. What are good positive and negative controls?

the correct answer to this question is #5

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.

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