1. The problem states the function $f(x) = |x + 1|$ and asks which limit statements about $f(x)$ are true. 2. Recall that the absolute value function $|y|$ returns the distance of $y$ from zero and is always non-negative. 3. Evaluate each limit: a. $\lim_{x \to 1^+} |x + 1| = |1 + 1| = |2| = 2$. True. b. $\lim_{x \to 1^-} |x + 1| = |1 + 1| = |2| = 2$. True. c. $\lim_{x \to -1^+} |x + 1|$. When $x \to -1$ from right, $x > -1$ so $x + 1$ is slightly positive, limit becomes $|0^+|=0$. So the limit is $0$ not $1$. False. d. $\lim_{x \to 1^-} |x + 1| = 2$ as shown in (b), not 0. False. e. $\lim_{x \to -1^-} |x + 1|$. When $x \to -1$ from left, $x + 1$ is slightly negative, but absolute value makes it positive close to 0. Thus limit is 0, not -1. False. 4. The correct limit statements are (a) and (b). Final answers: a and b are true; others are false.