Warmup: Let’s Practice Graphing Piecewise Functions Ourselves

Example Problem #2

Finding Limits Graphically PRE-CALCULUS UNIT 1 Day 2 Finding Limits Graphically

What is a limit? A limit describes how the output values of a function behave as input values approaches some given #, “c” Notation: Read “limit of f(x) as x approaches c is equal to L”

Kinds of limits THE Limit (double-sided limit) Left-hand limit Limit of f(x) as x approaches c from either direction. Only exists if left-hand and right-hand limits are the same. Left-hand limit Limit of f(x) as x approaches c from the left side. Right-hand limit Limit of f(x) as x approaches c from the right side.

Misconception #1 A function does not have to be defined at “c” in order for the limit to exist.

Misconception #2 If a function is defined at “c”, f(c) does not necessarily have to equal L.

Two Cases for When the Limit is D.N.E. (Does Not Exist) Behavior differs from the left and right Oscillating Behavior Ex/

Practice

Practice

Practice

Practice 13

Draw a graph such that

Draw a graph such that

Draw a graph such that

Draw a graph such that

Draw a graph such that

Draw a graph such that