Final answer:
To find where the function f(x) = x + 2 is positive or negative, inequalities x + 2 > 0 and x + 2 < 0 are solved, yielding positive interval (-2, ∞) and negative interval (-∞, -2), respectively.
The correct answer to the question is A) Positive: (-2, ∞), Negative: (-∞, -2).
Step-by-step explanation:
The question is about determining the positive and negative intervals for the function f(x) = x + 2.
To find out where the function is positive, we set f(x) to be greater than zero.
f(x) > 0 leads to x + 2 > 0. Solving this inequality, we get x > -2.
Hence, the function is positive for all x values greater than -2, which is the interval (-2, ∞).
Similarly, finding where the function is negative, we set f(x) to be less than zero: f(x) < 0.
This inequality translates to x + 2 < 0, solving which we get x < -2.
Therefore, the function is negative for all x values less than -2, corresponding to the interval (-∞, -2).
The correct answer for the student's MCQ is option A) Positive: (-2, ∞), Negative: (-∞, -2).