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#GRAPHING A PIECEWISE FUNCTION HOW TO#

Take 3 or more numbers for x if the piece is NOT a straight line. If the piece is a straight line, then 2 values for x are sufficient.

In each table, take more numbers (random numbers) in the column of x that lie in the corresponding interval to get the perfect shape of the graph.

If the endpoint is excluded from the interval then note that we get an open dot corresponding to that point in the graph. Include the endpoints of the interval without fail.

Make a table with two columns labeled x and y corresponding to each interval.

Write the intervals that are shown in the definition of the function along with their definitions.

For example, f(x) = ax + b represents a linear function (which gives a line), f(x) = ax 2 + bx + c represents a quadratic function (which gives a parabola), etc, so that we will have an idea of what shape the piece of the function would result in.

First, understand what each definition of the function represents.

Here are the steps to graph a piecewise function. Note that there is an example of a piecewise function’s inverse here in the Inverses of Functions section.We already know that the graph of a piecewise function has multiple pieces where each piece corresponds to its definition over an interval. 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. Obtaining Equations from Piecewise Function Graphs

#GRAPHING A PIECEWISE FUNCTION HOW TO#

How to Tell if a Piecewise Function is Continuous or Non-Continuous 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.Derivatives and Integrals of Inverse Trig Functions.Exponential and Logarithmic Differentiation.Differentials, Linear Approximation, Error Propagation.Curve Sketching, Rolle’s Theorem, Mean Value Theorem.Implicit Differentiation and Related Rates.Equation of the Tangent Line, Rates of Change.Differential Calculus Quick Study Guide.Polar Coordinates, Equations, and Graphs.Law of Sines and Cosines, and Areas of Triangles.Linear, Angular Speeds, Area of Sectors, Length of Arcs.Conics: Circles, Parabolas, Ellipses, 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/Odd, Extrema.Solving Radical Equations and Inequalities.

Solving Absolute Value Equations and Inequalities.Imaginary (Non-Real) and Complex Numbers.Solving Quadratics, Factoring, Completing Square.Introduction to Multiplying Polynomials.Scatter Plots, Correlation, and Regression.

Algebraic Functions, including Domain and Range.Systems of Linear Equations and Word Problems.Introduction to the Graphing Display Calculator (GDC).Direct, Inverse, Joint and Combined Variation.Coordinate System, Graphing Lines, Inequalities.Types of Numbers and Algebraic Properties.Introduction to Statistics and Probability.Powers, Exponents, Radicals, Scientific Notation.