Objective [1.11]-Problems
Understand what the terms “increasing” and “decreasing” mean with regards to a relationship. In particular be clear on
how a demand and supply relationships work. (i.e. are they increasing or decreasing, strictly or over only parts of the
domain) .
For each table of ordered pairs of a function indicate on which interval(s) it is increasing or decreasing. If it is “strictly”
say such. “Constant” is NOT an option.
Examples:
Table: Average price of a Home
t, Time (years, t=0 is 1990)
0
3
4
7
10
12
P=H(t), Price $ (thousands)
150
170
175
200
190
180
Answer: Strictly increasing on [0,7], strictly decreasing on [7,12]
Table: Average price of a Home
t, Time (years, t=0 is 1990)
0
3
4
7
10
12
P=H(t), Price $ (thousands)
150
170
170
200
190
180
Answer: increasing on [0,7], strictly decreasing on [7,12]
1. Table: Average price of a Home
T, Time (years, t=0 is 1990)
0
3
4
7
10
12
P=H(t), Price $ (thousands)
300
200
180
130
120
110
Answer: strictly decreasing on [0,12]
2. Table: Average price of a Home
T, Time (years, t=0 is 1990)
0
3
4
7
10
12
P=H(t), Price $ (thousands)
300
200
180
180
120
110
Answer: decreasing on [0,12]
3. Table: Average price of a Home
T, Time (years, t=0 is 1990)
0
3
4
7
10
12
P=H(t), Price $ (thousands)
300
200
180
180
190
220
Answer: decreasing on [0,7], strictly increasing on [7,12] or strictly decreasing on [0,4], increasing on [4,12]
4. Table: Average price of a Home
T, Time (years, t=0 is 1990)
0
3
4
7
10
12
P=H(t), Price $ (thousands)
300
400
350
370
380
390
Answer: increasing on [0,3], decreasing on [3,4], increasing on [4,12]
For the given functions indicate if they are increasing or decreasing. Note linear, exponential, and logistic functions are
either strictly one or the other over their entire the natural domains are all real numbers (except for a constant linear
function!)
Example:
q  G(b)  2b  5
5. G (t ) 
Ans: increasing
2
1  e0.1t
Ans: increasing
7. A(t )  (2)e0.1t Ans: increasing
t
8. H (t )  (4)1.1
Ans: increasing
9. q  G(b)  4  b
10 G (t ) 
1
1  e0.1t
Ans: decreasing
Ans: decreasing
H (t )  (2)0.9t
11.
Think twice!
Think twice!
Ans: increasing
12. Given the function, Q, graphed below. Indicate in interval notation when Q is increasing or decreasing.
Ans: Increasing on [0,1], decreasing on [1,3], increasing on [3,4]

y


Q


x





Many relationships seem to have some “law” of either increasing or decreasing (but not both) associated with them. For
the following relationships write that “law” out in English in any way you choose, then indicate if it means increasing or
decreasing. (good words to use are more/less, up/down, increases/decreases, raises/lowers,….can you think of others?)
Example:
Quantity demanded is a function of price
Ans: As the price goes up the quantity demanded goes down, decreasing
Note: there are other ways in English to indicate an increasing relationship! Can you be creative?
13. Quantity supplied is a function of price
Ans: As the price increases the quantity supplied increases, increasing
14. Pages left to read in a book is a function of the number of pages read.
Ans: The more pages read the less are left to read, decreasing
15. Course Grade is a function of time invested 
Ans: The more time one invests in study the higher their course grade, increasing!
16. The amount of new work you are given is a function of how competently you complete your present work.
Ans: The better and faster you do your job the more work they give you!, increasing.
I started a thread under math “Your relationship “law””. Please think of a relationship that as a “law” and at the thread
add your reply writing in the relationship and below your “law” just like the problems and answers above. No EC but
let’s share. It will be interesting (maybe even funny/silly) to see which relationships we think have “laws” with them. In
fact observing supposed relationship “laws” is one way a comedian can create humor. I can take what you post and use
them next quarter as examples or problems, and this quarter on an exam! In fact I am happy to have you make up
problems that I put on the exam. If you can make up problems that is one proof of mastery of an objective.