MAC 1105 Pre-Class Assignment: Multiple Representations of Functions
Read sections 2.1 ‘Graphs of Functions’ and 2.2 ‘Properties of Functions’ to prepare for class
In this week’s pre-requisite module, you covered the topics plotting points, intercepts and interval notations.
These are crucial skills needed for the conversation that we will be having this week about graph and
properties of functions.
Imagine the situation where you have a growing square that has side length s inches. As the square grows, the
length, 𝑠, gets bigger.
Consider the function that relates the perimeter, 𝑃, in inches, in terms of 𝑠, which is our independent variable.
Let’s name this function 𝑃(𝑠) where s is our input and 𝑃(𝑠) is our output.
In addition to the verbal description of perimeter above, we want to explore three additional representations
of our function 𝑃.
1) Algebraic Formula
a) What is the formula for the perimeter of a square?
b) We can then define 𝑃 by using function notation and an algebraic expression rule that is in terms of s
here:
𝑃(𝑠) =______________
2) Graphical Representation
a) Can 𝑠 be 0? Explain your answer.
b) Can 𝑠 be negative? Explain your answer.
c) What is the domain and range of 𝑃?
d) Draw the graph of 𝑦 = 𝑃(𝑠) here:
MAC 1105 Pre-Class Assignment: Multiple Representations of Functions
Read sections 2.1 ‘Graphs of Functions’ and 2.2 ‘Properties of Functions’ to prepare for class
e) So 𝑃 is a __________________ function.
3) Numerical Data Table
This will be a table filled with input values and output values. Fill in the missing values for 𝑃(𝑠).
Input
Output
1
3
4
2
8
28
40
Note that a numerical data table can only show finitely many input-output pairs at any one time.
While these four formats are very different looking, they all capture the same function, and are called the four
representations of f:




Verbal
Algebraic
Graphical
Numerical
4) Describe one advantage of the algebraic representation of f compared to its graphical representation?
5) Describe one advantage of the verbal representation of f compared to its numerical representation?