Forexample, we can talk about "flat" income tax versusa "graduated" income tax.Ī flat income tax would tax people at the same rate regardlessof their income.įor instance, let's say that the flat tax is 30% of your income.Some people think that flat tax is unfair for those in or nearthe poverty level because they are getting taxed at the same rateas those in a higher income bracket. Why study piecewise functions? Well, there are some real-lifepractical examples for studying piecewise linear functions. Our range runsfrom because we have no negative outputsfor the function. Note that this piecewise linear function is continuous andit is in fact a function because it passes the vertical line test.Notice, also that the domain is becausewe can substitute anything real number in for x. Graph of the absolute value function: y = |x| Now, let's graph this function using the points the chart aboveto plot our coordinates: Let's make a chart, substituting values in for x and solvingfor y = |x| as illustrated below. Why? Well, in essence, the absolute value is a distance-measuringdevice and distance is always positive even if you are walkingbackwards you are still going somewhere! The second part of thefunction seems confusing, because it seems like the answer shouldbe negative, but if x is less than zero to begin with, as it'sstated in the second part, then the answer is the opposite ofx, which is negative to begin with, so the answer is positive. So, whether x is positive, negative, or zero. The expression |x| is read "the absolute value of x." Graph of the Piecewise Function y = -x + 3 on theinterval Ī special example of a piecewise function is the absolute valuefunction that states: These functions do not share the samepoint at x = 0, as the first contains that point (0, 3), whilethe second piece contains the point (0, 1). For example, the graphof y = -x + 3 on the interval and the graph y = 3x + 1on the interval. Some piecewise functions are continuous like the one depictedabove, whereas some are not continuous. However,at the point where they adjoin, when we substitute 1 in for x,we get y = 5 for both functions, so they share the point (1, 5). In the first piece, the slopeis 2 or 2/1, while in the second piece, the slope is 0. Notice that the slope of the function isnot constant throughout the graph. The graph depicted above is called piecewise because it consistsof two or more pieces. Graph of the piecewise function y = 2x + 3 on theinterval (-3, 1) Since the graphs do not includethe endpoints, the point where each graph starts and then stopsare open circles Note that theyspan the interval from (-3, 5). The domain for this function is all the real numbers R while the range of this function is all the integers I.Consider the function y = 2x + 3 on the interval (-3, 1) andthe function y = 5 (a horizontal line) on the interval (1, 5).Let's graph those two functions on the same graph. The floor function also called the greatest integer function or integer value, gives the largest integer less than or equal to x. Two commonly used step functions are floor function and ceiling function. The graph looks staircase, they are a class of functions that have a graph that looks similar to a staircase. It is a piecewise function with a finite number of pieces. These functions are used a lot in the Electrical and Electronics engineering fields as they are used in Signals and systems. Represent this as a piecewise function and tell the price charged if Anil played the game for 13 minutes and Raju played for 20 minutes. Over 15 minutes costs Rs.15 plus Rs.1 per minute above 15 minutes.Over 6 and up to 15 minutes costs Rs.15.Question 2: An arcade game charges the following prices depending on the length of time: Question 1: Find the value of the following function at x = -2,10. Average and Instantaneous Rate of ChangeĪbsolute Value Function Evaluating Piecewise Functions.Class 11 NCERT Solutions - Chapter 3 Trigonometric Function - Exercise 3.1.Class 11 NCERT Solutions - Chapter 7 Permutations And Combinations - Exercise 7.1.Difference Between Mean, Median, and Mode with Examples.What is the Difference between Interactive and Script Mode in Python Programming?.ISRO CS Syllabus for Scientist/Engineer Exam.ISRO CS Original Papers and Official Keys.GATE CS Original Papers and Official Keys.
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