1. Section Continuity
2.2

2. A function f(x) is continuous at x = c if and only if all three of the
following tests hold:
f(x) is right continuous at x = -5
f(x) is continuous at x = -4
f(x) has infinite discontinuity at x = -3 [i, iii]
f(x) has point discontinuity at x = -2 [i, iii]
f(x) has infinite discontinuity at x = -1 [i, ii, iii]
f(x) is continuous at x = 0

3. Point Discontinuity [i, iii]
At x = 1
At x = 2
At x = 3
At x = 4
At x = 5
Point Discontinuity [i, iii]
Jump Discontinuity [i, ii, iii]
Continuous
Continuous
Point Discontinuity [i, (ii), iii]

4. continuous
continuous
pt. discontinuity at x = 0
inf. discontinuity at x = 1
pt. discontinuity at x = 3
continuous
inf. discontinuity at x = -3
jump discontinuity at x = 2

5. Find the value of a which makes the function below continuous

6. Find (a, b) which makes the function below continuous
As we approach x = = -a + b
As we approach x = = 3a + b

7. Consider the function
Find the value of k which makes f(x) continuous at x = 0
Since
, if k =1, the hole is filled.

8. Calculator Required
Let m and b be real numbers and let the function f be defined by:
If f is both continuous and differentiable at x = 1, then:

9. No Calculator
The function f is continuous at x = 1

10. Calculator Required
Which of the following is true about
I. f is continuous at x = 1
II. The graph of f has a vertical asymptote at x = 1
III. The graph of f has a horizontal asymptote at y = 1/2
I. f(1) results in zero in denominator….NO
II. Since x – 1 results in 0/0, it is a HOLE, NOT asymptote X X
III. X X

11. No Calculator
Which function is NOT continuous everywhere?
undefined at x = -1

12. Calculator Required
The graph of the derivative of a function f is shown below.
Which of the following is true about the function f?
I. f is increasing on the interval (-2, 1)
II. f is continuous at x = 0
III. f has an inflection point at x = 2 NO
YES NO
A. I B. II C. III D. II, III E. I, II, III

13. No Calculator
A B C D E. -2