3.5 Continuity and End Behavior

1. 3.5 Continuity and End Behavior Objectives: Determine whether a function is continuous or discontinuous. Identify the end behavior of functions. Determine whether a function is increasing or decreasing on an interval.

2. Discontinuous: A graph of a function you cannot trace without lifting your pencil. Graphs of Discontinuity. See pg.160 A function is continuous at x=c if it satisfies the following conditions:1.) the function is defined at c (f(c) exists)2.) the function approaches the same y-value on the left and right sides of x=c.3.) the y-value that the function approaches from each side is f(c). Continuity Test:

3. Ex. 1) Determine whether each function is continuous at the given x-value. a.) y = 3x² + x – 7 ; x = 1 b.) f(x) = (x² - 4)/(x + 2) ; x=-2 c.) f(x) = x² if x>-2 1/(x²-4) if x<-2

4. Continuity on an interval: A function f(x) is continuous on an interval iff. it is continuous at each number x in the interval. See example 2 in book…pg. 162 End Behavior: The behavior of f(x) as x becomes very large.

5. Ex. 3) Describe the end behavior of the functions f(x)=5x³ and g(x)=-5x³+4x²-2x+4. *End behavior of any polynomial function can be modeled by the function comprised solely of the term with the highest power of x and its coefficient. See page 163 Graph each function. Determine the interval(s) on which the function is increasing or decreasing. a.)f(x)=x²-7 b.) g(x)=-1/x c.) h(x)=5x³ + x² - x + 4 Ex. 4)*View graph from left to right to determine.