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The student will define and apply the properties of limits of functions. Limits will be

evaluated graphically and algebraically. This will include

a) limits of a constant;

b) limits of a sum, product, and quotient;

c) one-sided limits; and

d) limits at infinity, infinite limits, and non-existent limits. *

*AP Calculus BC will include l'Hopital's Rule, which will be used to find the limit of

functions whose limits yield the indeterminate forms: 0/0 and ∞/∞.

APC.3 The student will use limits to define continuity and determine where a function is

continuous or discontinuous. This will include

a) continuity in terms of limits;

b) continuity at a point and over a closed interval;

c) application of the Intermediate Value Theorem and the Extreme Value Theorem; and

d) geometric understanding and interpretation of continuity and discontinuity.

APC.4 The student will investigate asymptotic and unbounded behavior in functions. This will

include

a) describing and understanding asymptotes in terms of graphical behavior and limits

involving infinity; and

b) comparing relative magnitudes of functions and their rates of change.

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In this clip we go over how to graph a piece wise defined function comprised of two linear functions. We start out by going over the steps or strategies for graphing piecewise defined functions.

Steps for Graphing Piecewise functions(How to graph):

1) Plan: Use a number line to plan out which function goes where on the coordinate plane.

2) Graph Partition(s) & Label: On the coordinate system graph your partition(s) and label the sectioned planes accordingly using your set up in 1.

3)Graph each Piece: Graph the line of each function in their respective planes paying close attention to inclusion and exclusion at boundaries.

A piecewise function is a function made up of two or more pieces of functions defined on specified domains (intervals) of the piecewise function.

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