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.

Practice

Practice

Practice

Practice 12

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

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