1. 3-5 Continuity and End Behavior

2. Discontinuous: A function is discontinuous if you can not trace it without lifting your pencil.

3. Infinite Discontinuity – as the graph of f(x) approaches a given value of x, lf(x)l becomes increasingly greater
Jump Discontinuity – The graph of f(x) stops and then begins again with an open circle at a different range value for a given value of the domain.
Point Discontinuity – When there is a value in the domain for which f(x) is undefined, but the pieces of the graph match up
Everywhere Discontinuous – A function that is impossible to graph in the real number system is said to be everywhere discontinuous

4. Continuous Test
A function is continuous at x = c if it satisfies the following conditions:
1) The function is defined at c, in other words F(c) exists
2) The function approaches the same y-value on the left and right sides of x = c;

5. Determine if the function is continuous at the given point
f(x) = 3x2 +7; x = 1
2) F(x)= 𝑥−2 𝑥 2 −4 ; x = 2
3) F(x)= 1 𝑥 𝑖𝑓 𝑥>1 𝑥 𝑖𝑓 𝑥≤1 ; x=1

6. Continuity on an Interval
A function f(x) is continuous on an interval if and only if it is continuous at each number x in the interval.
4) 𝑓 𝑥 = 3𝑥−2 𝑖𝑓 𝑥>2 2−𝑥 𝑖𝑓 𝑥≤2 from -2<x<3

7. End Behavior
The behavior of f(x) as lxl becomes larger and larger (where is the graphing going?) Typically, a graph approaches ∞ 𝑜𝑟 −∞ We write the answer like "𝑓(𝑥)→∞ 𝑎𝑠 𝑥→∞”

9. Describe the end behavior of:
5) F(x) = -2x3
6) F(x) = -x3 +x2 –x+5

10. Increasing, Decreasing, and Constant Functions
A function f is increasing on an interval I if and only if for every a and b contained in I, f(a) < f(b) whenever a < b.
A function f is decreasing on an interval I if and only if for every a and b contained in I, f(a)> F(b) whenever a < b.
A function f remains constant on an interval I if and only if for every a and b contained in I, f(a) = f(b) whenever a < b

11. Determine the intervals each function is increasing or decreasing.
7)Graph f(x) = 3- (x-5)2
8) Graph f(x) = ½ lx+3l – 5
9)Graph f(x) = 2x3 + 3x2- 12x+ 3