### Exploring Piecewise Functions and LimitsIn this module, we will analyze the behavior of a piecewise function and determine its limits at specific points. The function is defined as follows:\[ f(x) = \begin{cases} 5 - x, & x < 3 \\3, & x = 3 \\2x - 3, & x > 3 \end{cases}\]### Graphical Representation of \(f(x)\)The graph provided alongside the function definition depicts the piecewise nature of \(f(x)\). Key components of the graph include:- A linear segment represented by \(5 - x\) for \(x < 3\).- A point at \(x = 3\) where \(f(x) = 3\).- Another linear segment denoted by \(2x - 3\) for \(x > 3\).The graph transitions through these different parts at \(x = 3\), reflecting the defined conditions.### Limit Analysis#### Part (a): Determine \(\lim_{x \to 3^-} f(x)\)Here, we focus on the limit of \(f(x)\) as \(x\) approaches 3 from the left-hand side (denoted as \(3^-\)). Select the correct answer:- **Option A**: \(\lim_{x \to 3^-} f(x) = \)(Simplify your answer, considering the expression \(5 - x\) as \(x\) approaches 3 from the left.)- **Option B**: The limit does not exist.#### Part (b): Determine \(\lim_{x \to 3^+} f(x)\)Next, consider the limit of \(f(x)\) as \(x\) approaches 3 from the right-hand side (denoted as \(3^+\)). Select the correct answer:- **Option A**: \(\lim_{x \to 3^+} f(x) = \)(Simplify your answer based on the expression \(2x - 3\) as \(x\) approaches 3 from the right.)- **Option B**: The limit does not exist.### Analysis ConclusionTo finalize the examination, compare the left-hand limit and the right-hand limit at \(x = 3\):- If both limits exist and are equal, we conclude that the

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Use the following function and its graph to answer parts (a) through (d) below. Let f(x) = 5-x, x<3 3, x = 3 O A. 2x 3 x>3. lim f(x)= (Simplify your answer.) X-3* OB. The limit does not exist. Ay 10- 0- C 0 10 a. Find lim f(x). Select the correct choice below and, if necessary, fill in the answer box in your choice. X-3* Q Find lim f(x). Select the correct choice below and, if necessary, fill in the answer box in your choice. x-3