This handout focuses on determining limits analytically and determining limits by looking at a graph. Draw a dotted vertical line for each of these values. Ap calculus ab worksheet 14 continuity to live for results would be to sentence myself to continuous frustration. Selection file type icon file name description size revision. Mathematics ii unit 5 step and piecewise functions part 1 piecewise functions day 1 piecewise functions domain range intervals that are constant. Finding limits of a piecewise defined function calculus i. We say that the limit of fx as x approaches a is equal to l, written lim x. This calculus video tutorial explains how to identify points of discontinuity or to prove a function is continuous discontinuous at a point by using the 3 step continuity test. When x 1, instead of having y 2 like we would expect, the point has jumped off the line up to y 3 how does a function like this affect what we know about limits. Leave any comments, questions, or suggestions below.
I start out class with a 15minute minilesson, giving my students some basic examples of what todays lesson will be about. On graphing piecewise functions to graph a piecewise function, it is a good idea to follow these steps. Limits algebraically eleanor roosevelt high school. Optional video piecewise functions in a calculator. A step function is discontinuous cannot draw a step function without removing your pencil from your paper. Hugh prather for problems 14, use the graph to test the function for continuity at the indicated value.
Suppose you have the graph of a piecewise defined function. Then, evaluate the graph at the specified domain values. Limits will be formally defined near the end of the chapter. My only sure reward is in my actions and not from them. District programs, activities, and practices shall be free from discrimination based on race, color, ancestry, national origin, ethnic group identification, age, religion, marital or parental status, physical or mental disability, sex, sexual orientation, gender, gender identity or expression, or genetic information. Finding limits of a piecewise defined function calculus i tutorial, by dave collins i. Create the worksheets you need with infinite calculus.
Limits are used to define continuity, derivatives, and integral s. Limits of piecewise functions practice khan academy. Given the rules for a piecewise function, find limits of that function. This value is called the left hand limit of f at a. Provided by the academic center for excellence 1 calculus limits november 20 calculus limits images in this handout were obtained from the my math lab briggs online ebook. Limits of piecewisedefined functions worksheet 2 pages hiccup function limit notes 6 pages, summary briggs textbook interactive figures hole, cos1x limit of the slope of a function interactive1, interactive2 properties of limits notes limits of a piecewisedefined function 2 worksheet indeterminate forms worksheet. Functions, graphs, and limits piecewise functions and limits. We will use limits to analyze asymptotic behaviors of functions and their graphs. Use the graph of the function fx to answer each question. The student will determine the limit of a function by numerical means and will illustrate the concept with a graph. Properties of limits will be established along the way. There are multiple cases for finding the limit of a piecewise function.
From the algebraic representation of the function lets start with the graph. If x c is at a restricted value or where the function changes behaviors, consider both left and righthand limits. Even when the limits of two functions at some point do not exist, the limit of their sum or product might still exist. The constant pieces are observed across the adjacent intervals of the function, as they change value from one interval to the next. Continuity of a function at a point and on an interval will be defined using limits. Limits of piecewise functions in exercises, use the graph to determine the limit, if it exists. A limit is the value a function approaches as the input value gets closer to a specified quantity. Find the following limits for the piecewise function. Name period worksheet piecewise functions 3x 5, x 4. Page 1 of 2 114 chapter 2 linear equations and functions piecewise functions representing piecewise functions up to now in this chapter a function has been represented by a single equation. Piecewise functions are simply functions that have been broken into 2 or more pieces, where each piece is a portion of the graph. Find the slope, xintercept, and yintercept of the line 3x 2y 4. The function is continuous at all points of its domain.
Youve been inactive for a while, logging you out in a few seconds. Study the following functions and determine if they are continuous. This worksheet is designed to replace a lecture on the topic of using function notation, evaluating functions, and piecewisedefined functions. Now well shake things up a bit by taking limits with piecewisedefined functions. We shall study the concept of limit of f at a point a in i. We say lim x a f x is the expected value of f at x a given the values of f near to the left of a. If x c is inside an interval but is not a restricted value, the limit is fc. If the limit does not exist or the value of the function is undefined, indicate this. How to evaluate limits of piecewisedefined functions explained with examples and practice problems explained step by step. Find the equation of the line that passes through 1. Mathematics ii unit 5 step and piecewise functions part 1. If youre behind a web filter, please make sure that the domains.
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