Unit 512: End Behavior of Polynomial Functions Polynomial: A polynomial is an algebraic expression that is composed of variables, exponents End Behavior:behavior of the graph at the "ends" of the x-axis (left end and right end) rote Pot mom!appen non Degrenced Confficlent positive Ind Behavior: End Bebevien non f(x)arrow +infty f(x)arrow -infty ax-1-9) y=x^2 isxarrow -infty y=x^2 a f(x)arrow +infty f(x)arrow +infty msxarrow +infty xarrow +infty Domokistl real numbers Domeins of real numbers Range:ell real numbers 2 minimum Range, nill roel numbers Degree; even Degreerodd Coefficlents negative Laiding Conflidents negative Ind Coharter: f(x) win f(x)arrow +infty asxarrow -infty assess ax-400 isxarrow +infty Dompin: ell real numbers Range:all real numbers s meximum Reager all real numbers

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Unit 512: End Behavior of Polynomial Functions Polynomial: A polynomial is an algebraic expression that is composed of variables, exponents End Behavior:behavior of the graph at the "ends" of the x-axis (left end and right end) rote Pot mom!appen non Degrenced Confficlent positive Ind Behavior: End Bebevien non f(x)arrow +infty f(x)arrow -infty ax-1-9) y=x^2 isxarrow -infty y=x^2 a f(x)arrow +infty f(x)arrow +infty msxarrow +infty xarrow +infty Domokistl real numbers Domeins of real numbers Range:ell real numbers 2 minimum Range, nill roel numbers Degree; even Degreerodd Coefficlents negative Laiding Conflidents negative Ind Coharter: f(x) win f(x)arrow +infty asxarrow -infty assess ax-400 isxarrow +infty Dompin: ell real numbers Range:all real numbers s meximum Reager all real numbers

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Based on the picture details provided, let's analyze the given information step by step to answer the questions about the polynomial function f(x).Step 1: Identify the Degree and Leading CoefficientSince the graph of the function f(x) passes through the origin (0,0) and is located in the first and second quadrants, with the curve first decreasing and then increasing, we can infer that the function has an odd degree and a positive leading coefficient. This is because odd-degree polynomials with a positive leading coefficient start from the bottom left (negative infinity on the y-axis when x approaches negative infinity) and end at the top right (positive infinity on the y-axis when x approaches positive infinity).Step 2: Determine the End BehaviorThe end behavior of a polynomial function is determined by its degree and leading coefficient. For an odd-degree polynomial with a positive leading coefficient, as x approaches negative infinity, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches positive infinity.Step 3: Define the Domain and RangeThe domain of a polynomial function is the set of all possible x-values that can be input into the function. For any polynomial function, the domain is all real numbers, which can be written as (-∞, ∞).The range of a polynomial function is the set of all possible y-values that the function can output. Based on the graph described, since the function decreases to negative infinity and increases to positive infinity, the range is also all real numbers, which can be written as (-∞, ∞).Answer:- Degree: The degree is odd.- Leading Coefficient: The leading coefficient is positive.- End Behavior: As x → -∞, f(x) → -∞; as x → ∞, f(x) → ∞.- Domain: (-∞, ∞)- Range: (-∞, ∞)

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