1. Assigned work: pg 51 #4adef, bcdf,7,8,10-13 A continuous curve is a curve without breaks, holes or jumps. Usually if we talk about a curve being discontinuous it is at a specific point. These are discontinuous…. HOLEJUMPASYMPTOTE S. Evans

2. 1.6 Continuity S. Evans Conditions for Continuity: 1)must exist 2) must exist (i.e. LHL=RHL) 3) (i.e. condition 1 = condition 2) Note: For all polynomials so all polynomials are continuous.

3. 1.6 Continuity S. Evans In the following examples state which condition fails: cond 1cond 2cond 1cond 3

4. 1.6 Continuity When determining if a function is continuous you need to know where you should look for discontinuities….. For Rational functions: Look at when the denominator equals 0. If discontinuous, would fail condition 1 and 2 If discontinuous, would be a hole or asymptote S. Evans

5. 1.6 Continuity For Piecewise Functions: Look at the extreme domain values If discontinuous, could fail condition 1, 2, and/or 3. If discontinuous, would be a jump or hole. NOTE: We are fussy about format for continuity so show ALL conditions in your work when showing if function is continuous or not. S. Evans

6. 1.6 Continuity Rational Function Examples: Ex. 1:For what values of x is f(x) discontinuous. Show why, state which condition fails and what discontinuity you have. a) S. Evans Hole at x = -1 Asymptote at x = 2 We need to show conditions where denominator is = 0 (see next slide)

7. 1.6 Continuity S. Evans So f(x) is discontinuous So f(x) is discontinuous at x = -1 (hole at -1,-1/3)at x = 2 (vert. asymptote)

8. 1.6 Continuity S. Evans So f(x) is discontinuous at x = 5 (vert. asymptote) b) Asymptote at x = 5 Now show conditions

9. 1.6 Continuity Piecewise Function Examples: Ex. 2:For what values of x is f(x) discontinuous. Show why, state which condition fails and what discontinuity you have. a) S. Evans Ask yourself where might f(x) be discontinuous? Look at domains – notice 1 & -1.

10. 1.6 Continuity S. Evans So f(x) is continuous So f(x) is discontinuous at x = -1 at x = 1 (jump)

11. 1.6 Continuity b) S. Evans Ask yourself where might f(x) be discontinuous? Look at domains i.e. 0 So f(x) is discontinuous at x= 0 (hole at 0,1) Now Graph it