Limits Analysis of a Function Graph
The image shows a graph of a function \( y = f(x) \) with various labeled points and behaviors around certain x-values, which we are asked to analyze to determine the limits.
a) \( \lim_{x \to -3^-} f(x) = \)
The graph approaches the y-value as x approaches -3 from the left side (negative side), which looks to be \( -\infty \).
b) \( \lim_{x \to -3^+} f(x) = \)
When x approaches -3 from the right side (positive side), the graph approaches a finite y-value, which appears to be 2.
c) \( \lim_{x \to 2^-} f(x) = \)
As x approaches 2 from the left side, the graph approaches the y-value which appears to be 3.
d) \( \lim_{x \to 2^+} f(x) = \)
When x approaches 2 from the right side, the graph is again approaching the y-value of 3.
e) \( \lim_{x \to \infty} f(x) = \)
As x goes to infinity, the y-value that the graph tends toward seems to be 0, which represents a horizontal asymptote at y = 0.
So the answers are:
a) \( -\infty \)
b) 2
c) 3
d) 3
e) 0
