TOPIC 1.2b
: Continuity and Increasing/Decreasing
Activity 1. Use the terms below to analyze functions A – C.
Constant
function
Increasing
function
Decreasing
function
Removable
DISCONTINUITY
y
–5
–4
–3
–2
Local
Maximum
y
5
5
4
4
3
3
2
2
1
1
–1
–1
Infinite
DISCONTINUITY
1
2
3
4
5
x
–15 –12 –9
–6
–3
–1
–2
–2
–3
–3
–4
–4
–5
y
8
7
6
5
4
3
2
1
3
6
9
12
15
x
–8 –7 –6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
–6
–7
–8
–5
A.
Local
Mininum
B.
1 2 3 4 5 6 7 8
x
C.
2. Graph analysis Find the following for the graph of the function given below:
y
x-int: _____________________
8
Y- intercept(s): _____________________
4
Domain: ___________________
–8
–4
4
–4
–8
8
x
Range:
___________________
Inc __________
Dec __________ Const________
A.
Local Min Max at x = _______
Discontinuity _____________ at____________
y
x-int: _____________________
12
10
Y- intercept(s): _____________________
8
6
Domain: ___________________
4
2
–12 –10 –8 –6 –4 –2–2
2
4
6
8 10 12
x
–4
Range:
___________________
Inc __________
–6
Dec __________ Const________
–8
Local Min Max at x = _______
–10
–12
B.
Discontinuity _____________ at____________
y
x-int: _____________________
12
10
Y- intercept(s): _____________________
8
6
Domain: ___________________
4
2
–12 –10 –8 –6 –4 –2–2
2
4
6
–4
–6
8 10 12
x
Range:
___________________
Inc __________
Dec __________ Const________
–8
–10
Local Min Max at x = _______ (estimate)
–12
C.
Discontinuity _____________ at____________
3. Game: In groups of 4 students, graph examples of functions with:
a) 2 removable discontinuities
b) 1 removable and 1 infinite discontinuity
c) Has a Local Max at x = -4, and Local Min at x = 4, is constant for x  3, 2


d) “mystery” graph to be described by members of another group (it should display at least 3 terms).