Basic HTML Version
© 2014 Pacific Crest
103
2.5
Analyzing a Function
P
urpose
The role this topic plays in quantitative reasoning
Many variables or quantities in life are functions of other variables. Being able to analyze the behavior
of such functions, both algebraically and graphically, can explain a lot about phenomenon and may be
used to predict future behavior as well. Functions are at the heart of mathematical modeling. They are
used in probability distribution, statistics, financial analysis, and throughout this course and life.
L
earning Goals
What you should learn while completing this activity
1. Convert an equation into a functional definition (if possible)
2. Effectively graph a function by hand or on a computer
3. Analyze and interpret a function from its graph
D
iscovery
Finding out for yourself
Which of the following six function types (linear, logarithm, rational, cyclical/periodic, quadratic,
exponential) best describe the phenomena in the phenomena table? Select 10 of the phenomena to match
to function types. Note that not all of the phenomena are represented by one of the six function types so
you will receive extra credit if you identify one that isn’t and locate a graph of its function type!
-10
10
y
1
1
6
-6
x
f(x) =
2
x
+ 3
-4
-6
2
1
15
7
f(x) =
log
2
(x)
y
x
12
-12
-8
8
1
1
y
x
f(x) =
(
x
– 2)(
x
+ 3)
(
x
+ 1)(
x
– 5)
linear
logarithm
rational
7
-7
-5
4
1
1
y
x
y
= 1
y
= –3
f(x)
=2
•
sin(
x
– 5) –1
-10
10
y
1
1
6
-6
x
(–3, –4)
f(x)
= 2
x
2
+ 12
x
+14
12
y
1
11
-2
0.5
-7
x
f(x) =
3
•
2
x
cyclical/periodic
quadratic
exponential