Math 1201 Section 5.2: Function Notation
Function Notation
 When a relation is a function, there exists only one value of the
dependent variable (y) for every value of the independent
variable (x). (ie. There can be no repeated values in the domain)
 When the relation between two values is a function, we can write
the relation (equation) in two ways:
o An equation in two variables.
Ex. C = 5n + 15
where C represents cost($) and n
represents number of cds
o As function notation (can only be used if a relation is a
function)
Ex continued…
Number of cds, n
Cost ($)
1
20
2
25
3
30
4
35
5
40
Since for each number of cds you buy, there can only be one cost, this
relation is a function. Also, since the cost depends on the number of
cds bought, we say that “the cost is a function of n” and we can write it
in function notation as follows:
C(n) = 5n + 15
We say “C of n is equal to 5 times n plus 15”
Ex 2
T = -2k +20,
where k is the altitude (km) and T is the temp.
(Celcius)
Since temperature depends on the number of km travelled, we say that
“temperature is a function of altitude” and we write:
T(k) = -2k + 20 We say “T of k is equal to minus 2 times k plus 20”
Ex3: When one thing affects another we often use the term “function”
in everyday speech. For example, we might say,
“The mark you receive on a test is a function of how much you study”,
meaning your mark can depend largely on how much you study.
Calculations involving Function Notation:
1. Given the function,
a. f(3)
f(x) = -3x + 6, find:
b. f(-20)
2. Given the function, g(x) = 6x + 10, determine x when:
a. g(x) = 40
b. g(x) = -8
3. The equation V = -0.08d + 50 represents the volume, V litres, of
gas remaining in a vehicle’s tank after travelling d kilometers. The
gas tank is not refilled until it is empty.
a. Describe the function. Write the equation in function
notation.
b. Determine the value of V(600). What does this number
represent?
c. Determine the value of d when V(d) = 26. What does this
number represent?
Students should complete: p. 272 # 14bc, 15ai, bii, 16, 17, 18ab, 19ai, bi