![]() Our Year 11 Maths Adv Matrix courses are the expert guided solution to your Maths problems. Want to avoid your Year 11 Maths Advanced progress looking like a Piecewise Function? Example 1: x 1, if x 1 f (x) - 3, if x > 1 b We have two different equations (or pieces) joined together under the function symbol f (x). This is denoted by using a closed or open circle as you would have done when graphing inequalities on a number line. Definition: A piecewise function is a function that is defined by two or more equations over a specific interval. 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. 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: 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 Ideal for students just starting to understand the key concepts of functions. Definition and Evaluating Piecewise Functions Worksheet to introduce Piecewise Functions including finding domain and range, increasing or decreasing ranges, identifying as a function, intervals, y-intercept, step functions, interpret key features and describe quantitative relations.
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