Want to avoid your Year 11 Maths Advanced progress looking like a Piecewise Function? This is denoted by using a closed or open circle as you would have done when graphing inequalities on a number line.
It is important to indicate which point is a part of the function, and which is not, as we cannot have multiple \(y\) values for the same \(x\) value (a piecewise function is still a function). Sketch each function in their respective domains, and you have sketched the piecewise function!Īn important feature to note is the discontinuity, where the different parts of the function do not meet each other, as at \(x = 0\) in our example.
Piecewise functions worksheet how to#
These are all simple functions and should be recognised as a parabola and \(2\) straight lines, which we already know how to sketch. \(y = 3\) when \(x\) is between \(0\) and \(3\)Īnd now we have \(3\) functions defined over \(3\) separate domains. This may look complicated, but like our first example we can break this down to: Rewrite the function using these two expressions and simplify: Practice problems: Rewrite the following absolute value functions as piecewise-defined. Sketching piecewise functions can similarly be made quite easy by considering it as sketching multiple separate functions.Īs an example, we will go through the process of sketching: This is illustrated by the discontinuity in the next section. The simplest example to illustrate this is the absolute value function, defined by: Students should already be familiar with function notation, domain and range, inequalities and evaluating and sketching polynomials.ĭefinition and Evaluating Piecewise FunctionsĪ piecewise function is a function defined separately for different intervals of \(x\) – values (different domains). Solve practical problems involving a pair of simultaneous linear and/or quadratic functions algebraically and graphically, with or without the aid of technology including determining and interpreting the break-even point of a simple business problem.Model, analyse and solve problems involving quadratic functions.NESA expects students to demonstrate proficiency in the following syllabus outcomes Graph the following piecewise functions for the specified domain. Definition and Evaluating Piecewise Functions Students understand that the graph of a function f is the graph of the equation y f(x) New York State Common Core Math Algebra I, Module 3, Lesson 15 Worksheets for Algebra I, Module 3, Lesson 15 (pdf) Problem Set Sample Solutions.
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