Lesson 3
Gr. 10 Pre-Calc/Applied Math
Unit 5 –Relations & Functions
R8 – Using Function Notation
Lesson Focus: To develop the concept of a function.
Investigate: Check out the “Input/Output Machine” below.
1. What is the rule for the Input/Output machine above?
You multiply by 2, then you add 3.
2. Which numbers would complete the table below for the machine?
Gr. 10 Pre-Calc/Applied
Input
Output
1
5
2
7
3
9
4
11
5
13
Unit 5, Lesson 3
We can think of a function as an input/output machine.
The input can be any number in the domain.
The output depends on the input number.
Therefore:

the input (domain) is the independent variable (x axis)

the output (range) is the dependent variable (y axis)
Function Notation
Read p. 268 & 269
The equation V = 0.25q represents the value ($) depending on the number of
quarters.
For this situation:
Input: q, quarters
Output: V, value
Dependent variable: value
Independent variable: number of quarters
Function notation: V(q) = 0.25q
Read as: “V of q is equal to 0.25q”
V(3) represents the value of the function when q = 3.
V(3) = 0.25(3)
V(3) = 0.75
The value of 3 quarters is $0.75.
Gr. 10 Pre-Calc/Applied
Unit 5, Lesson 3
Ex. 1 For the function f(x) = 2x + 3, determine f(2) and f(-5).
f(2) = 2(2) + 3
f(-5) = 2(-5) + 3
f(2) = 7
f(-5) = -7
Writing Equations as Functions
Any function that can be written as an equation in two variables can be written in
function notation. If the variables in the equation give context to the question,
for example: cost to rent a hall depends on the number of people
C = 300 + 25n
This equation can be written as a function:
C(n) = 300 + 25n
But if the equation is not related to a context:
Ex.
y = 4x + 5
the function is written as
f(x) = 4x + 5
Conversely, an equation written in function notation can be written as an equation in
2 variables.
Ex. C(n) = 400 + 30n
can be written as C = 400 + 30n
Letters other than f are used to name functions. For example, g, h, or k.
Ex. g(x) = -2x – 8 can be written as y = -2x - 8
Ex. 2 Represent the following equations as functions.
State which variables represent the domain and the range.
a. d = 4t + 5
Function: d(t) = 4t + 5
Domain: t
Range: d(t)
b. y = -2x + 7
Function: f(x) = -2x + 7
Gr. 10 Pre-Calc/Applied
Domain: x
Range: f(x)
Unit 5, Lesson 3
Ex. 3 Represent the following functions as equations.
State which variables represent the domain and the range.
a. f(x) = 5x – 2
Equation: y = 5x -2
Domain: x
Range: y
b. h(x) = -6x + 9
Equation: y = -6x + 9
Domain: x
Range: y
Ex. 4 The equation V = -0.08d + 50 represents the volume, V litres, of gas
remaining in a vehicle’s tank after travelling d kilometres. The gas tank is
not refilled until it is empty.
a. Describe the function. Write the equation in function notation.
“The volume of gas remaining is a function of the distance travelled.”
V(d) = -0.08d + 50
b. Determine the value of V(600). What does this number represent?
V(600) = -0.08(600) + 50
V(600) = 2
This means that when the car has travelled 600 km, the volume of
gas remaining in the tank is 2L.
c. Determine the value of d when V(d) = 26. What does this number
represent?
V(d) = -0.08d + 50
26 = -0.08d + 50
26 – 50 = d
-0.08
d = 300
This means that when there is 26 L left in the tank, the vehicle has
driven 300 km.
Assignment
Gr. 10 Pre-Calc/Applied
Do #6, 7, 14 – 23 p. 271
Unit 5, Lesson 3
Lesson 3
Gr. 10 Pre-Calc/Applied Math
Unit 5 –Relations & Functions
Student Copy
R8 – Using Function Notation
Lesson Focus: To develop the concept of a function.
Investigate: Check out the “Input/Output Machine” below.
1. What is the rule for the Input/Output machine above?
2. Which numbers would complete the table below for the machine?
Input
Output
1
2
9
4
13
Gr. 10 Pre-Calc/Applied
Unit 5, Lesson 3
We can think of a function as an input/output machine.
The input can be any number in the ___________.
The output depends on the ________ number.
Therefore:

the input (_________) is the ______________ variable (__ axis)

the output (________) is the ______________ variable (__ axis)
Function Notation
Read p. 268 & 269
The equation V = 0.25q represents the value ($) depending on the number of
quarters.
For this situation:
Input: __, __________
Output: __, __________
Dependent variable: ____________
Independent variable: ___________________
Function notation: V(q) = 0.25q
Read as: “V of q is equal to 0.25q”
V(3) represents the value of the function when q = ___.
V(3) = _________
V(3) = _________
The value of 3 quarters is _________.
Gr. 10 Pre-Calc/Applied
Unit 5, Lesson 3
Ex. 1 For the function f(x) = 2x + 3, determine f(2) and f(-5).
Writing Equations as Functions
Any function that can be written as an equation in two variables can be written in
function notation. If the variables in the equation give context to the question,
for example: cost to rent a hall depends on the number of people
C = 300 + 25n
This equation can be written as a function:
C(n) = 300 + 25n
But if the equation is not related to a context:
Ex.
y = 4x + 5
the function is written as
f(x) = 4x + 5
Conversely, an equation written in function notation can be written as an equation in
2 variables.
Ex. C(n) = 400 + 30n
can be written as C = 400 + 30n
Letters other than f are used to name functions. For example, g, h, or k.
Ex. g(x) = -2x – 8 can be written as y = -2x - 8
Ex. 2 Represent the following equations as functions.
State which variables represent the domain and the range.
a. d = 4t + 5
Function: ____________________
Domain: ___
Range: ___
b. y = -2x + 7
Function: ____________________
Domain: ___ Range: ___
Ex. 3 Represent the following functions as equations.
State which variables represent the domain and the range.
Gr. 10 Pre-Calc/Applied
Unit 5, Lesson 3
a. f(x) = 5x – 2
Equation: ________________
Domain: ___ Range: ___
b. h(x) = -6x + 9
Equation: _________________
Domain: ___ Range: ___
Ex. 4 The equation V = -0.08d + 50 represents the volume, V litres, of gas
remaining in a vehicle’s tank after travelling d kilometres. 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?
Assignment
Gr. 10 Pre-Calc/Applied
Do #6, 7, 14 – 23 p. 271
Unit 5, Lesson 3