Warm-Up
OGrab a white board with
a partner and the ½
yellow sheet. Have fun
with the white board
Continuity
Section 1.4
3 types of discontinuities: jump, point, infinite
O A function f is continuous at x = c if there is no
interruption in the graph of f at c such as a hole,
jump, or gap.
O Functions can be continuous at a point, on an
open interval and on a closed intervals.
Watch closely!
Checkout our worksheet
Open Intervals and Discontinuity
Watch out for piece-wise and rational functions.
Removable Discontinuity: points because they can
be refilled by simply restating a domain.
Non-Removable Discontinuity: infinite, jumps
because you can’t fix this domain whatsoever.
Discussing
Continuity
Remember
this must
happen!
What did you find to be an effective trick to
determine continuity?
Semi -Challenge
O Determine the value of c such that the
function is continuous on the entire real line.
𝑓 𝑥 =
𝑥 + 3,
𝑐𝑥 + 6,
𝑥≤2
𝑥>2
Is this function continuous on its
domain[-1,1] which is closed?
𝑓 𝑥 = 1 − 𝑥2
How can we test on a closed
interval?
Properties of Continuity
What this says is that if f and g are both continuous functions
by themselves at c, when they do they above operations
together, then the resulting new function is also continuous
no matter what and you don’t need to test.
Applying Properties of Continuity
Which, if any, are continuous functions in their
domains?
Why or why not?
If Time Permits
O Begin the IVT and EVT Exploration Exercise
(or else it’s homework but we need to watch
our pacing)
Homework
O Section 1.4 #8-20 even, 29-32 all, #37-51 odd,
57-64 all, 80-85 all
O QUIZ Friday on 1.2, 1.3
O Expect a quick quiz over continuity and its
definition and testing for it next Tuesday.