Question - Limits Analysis of a Function Graph
mathhorizontal asymptotelimits analysis function graphlimit approaching valuesx-value behavior analysis
Solution:
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) 2c) 3d) 3e) 0
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