Sometimes, you’ll be given piecewise functions and asked to evaluate them in other words, find the \(y\) values when you are given an \(x\) value.The median home value in Westby, WI is $ 225,000. See, not so bad, right? Evaluating Piecewise Functions \(\displaystyle f\left( x \right)=\left\\) graph, we can just use a closed circle as if it appears on both functions. Note that there is an example of a piecewise function’s inverse here in the Inverses of Functions section. Thus, the \(y\)’s are defined differently, depending on the intervals where the \(x\)’s are. The easiest way to think of them is if you drew more than one function on a graph, and you just erased parts of the functions where they aren’t supposed to be (along the \(x\)’s). Piecewise functions (or piece-wise functions) are just what they are named: pieces of different functions (sub-functions) all on one graph. Introduction to Piecewise Functions Absolute Value as a Piecewise Function Evaluating Piecewise Functions Transformations of Piecewise Functions Graphing Piecewise Functions Piecewise Function Word Problems How to Tell if a Piecewise Function is Continuous or Non-Continuous More Practice Obtaining Equations from Piecewise Function Graphs Introduction to Piecewise Functions Applications of Integration: Area and Volume.Exponential and Logarithmic Integration.Riemann Sums and Area by Limit Definition.Differential Equations and Slope Fields.Antiderivatives and Indefinite Integration, including Trig Integration.Derivatives and Integrals of Inverse Trig Functions.Exponential and Logarithmic Differentiation.Differentials, Linear Approximation, and Error Propagation.Curve Sketching, including Rolle’s Theorem and Mean Value Theorem.Implicit Differentiation and Related Rates.Equation of the Tangent Line, Tangent Line Approximation, and Rates of Change.Basic Differentiation Rules: Constant, Power, Product, Quotient, and Trig Rules.Differential Calculus Quick Study Guide.Polar Coordinates, Equations, and Graphs.Law of Sines and Cosines, and Areas of Triangles.Linear and Angular Speeds, Area of Sectors, and Length of Arcs.Conics: Circles, Parabolas, Ellipses, and Hyperbolas.Graphing and Finding Roots of Polynomial Functions.Graphing Rational Functions, including Asymptotes.Rational Functions, Equations, and Inequalities.Solving Systems using Reduced Row Echelon Form.The Matrix and Solving Systems with Matrices.Advanced Functions: Compositions, Even and Odd, and Extrema.Solving Radical Equations and Inequalities.Solving Absolute Value Equations and Inequalities.Imaginary (Non-Real) and Complex Numbers. ![]()
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