C957 Modules and Lessons
Review With Practice Questions
And Correct Answers| C957
Applied Algebra Review 2026-
2027/ Lesson 11-78 Review of Key
concepts
C957 module 3 Course review
,Rate of Change
Module 3: Deriving Conclusions Based on Data
Lesson 11: Interpreting Tables of Data
Learning Objectives
• Given a table of data, interpret the table as both functions and inverse functions in context.
Lesson Introduction
Did you know that Tim Berners Lee published the world's very first website, back in the summer of 1991? Since
those good old days, the internet has grown by leaps and bounds, just the way a good financial investment
grows over time.
Sometimes it can be helpful to look at data visually, like on a graph. Sometimes, however, using a table can be
more helpful. In this lesson, you will compare the same information in tables, graphs, and function notation to
see how one view can shed light on another.
Paired Data Points
Begin by looking at these numbers in the following table. (Note that the number of users in each case is in
millions, so, for example, the number 400 for the year 2000 is actually 400,000,000 users. The number 2009 for
the year 2010 is actually 2,009,000,000—over two billion users!)
This is good information, but does it "paint a picture" for you? A graph might be a better way to see the
information more visually.
Begin by identifying the pairs of data points in the table. Each pair contains a year and the corresponding
number, in millions, of internet users at that time. Note that the convention is to write the
independent variable first—in this case the year—and to write the dependent variable second. So the ordered
pairs are: (1995, 40), (2000, 400), (2005, 1025), (2010, 2009), and (2015, 3225).
Next, construct a graph with its x-axis representing the passage of time in 5-year increments and its y-axis
representing the number of internet users in millions. Finally, plot the pairs of points you just listed. The
following graph depicts what you should have plotted:
1
, Point A on the graph is equivalent to the pair of data points (1995, 40), and also the same as the first row in the
original table.
B is the same as the pair (2000, 400) and the second row in the table. C is the same as (2005, 1025) and the third
row in the table; D, the same as (2010, 2009) and the fourth row; and E, the same as (2015, 3225) and the fifth
row.
Applying Function Notation
Examine the following table.
You probably notice a difference between this table and the last one. Rest assured that this one contains the
exact same data, but it is been renumbered to make things a bit easier to deal with. Here, Year 1 represents the
calendar year 1995 and the number of users are expressed in billions, not millions. (To convert into billions,
simply divide the usage numbers in millions by 1000.)
To apply function notation to this data, assign Year as the input variable to the function f. The function f has an
output variable, notated f(YEAR), which in this case is the number of internet users (in billions). Each
output f(YEAR) must be a single value paired to each input. The input variable Year is placed inside the pair of
parentheses of f, and does not refer to multiplication. Now you can
write f(YEAR) = Worldwide internet users in billons.
Here is a key point: The data are exactly the same as they were previously in the original table, the ordered
pairs, and the graph. Nothing has changed except the notation of the ordered pairs. It is sometimes very helpful
to rescale a graph, as in the following graph to make it easier to understand.
2
Review With Practice Questions
And Correct Answers| C957
Applied Algebra Review 2026-
2027/ Lesson 11-78 Review of Key
concepts
C957 module 3 Course review
,Rate of Change
Module 3: Deriving Conclusions Based on Data
Lesson 11: Interpreting Tables of Data
Learning Objectives
• Given a table of data, interpret the table as both functions and inverse functions in context.
Lesson Introduction
Did you know that Tim Berners Lee published the world's very first website, back in the summer of 1991? Since
those good old days, the internet has grown by leaps and bounds, just the way a good financial investment
grows over time.
Sometimes it can be helpful to look at data visually, like on a graph. Sometimes, however, using a table can be
more helpful. In this lesson, you will compare the same information in tables, graphs, and function notation to
see how one view can shed light on another.
Paired Data Points
Begin by looking at these numbers in the following table. (Note that the number of users in each case is in
millions, so, for example, the number 400 for the year 2000 is actually 400,000,000 users. The number 2009 for
the year 2010 is actually 2,009,000,000—over two billion users!)
This is good information, but does it "paint a picture" for you? A graph might be a better way to see the
information more visually.
Begin by identifying the pairs of data points in the table. Each pair contains a year and the corresponding
number, in millions, of internet users at that time. Note that the convention is to write the
independent variable first—in this case the year—and to write the dependent variable second. So the ordered
pairs are: (1995, 40), (2000, 400), (2005, 1025), (2010, 2009), and (2015, 3225).
Next, construct a graph with its x-axis representing the passage of time in 5-year increments and its y-axis
representing the number of internet users in millions. Finally, plot the pairs of points you just listed. The
following graph depicts what you should have plotted:
1
, Point A on the graph is equivalent to the pair of data points (1995, 40), and also the same as the first row in the
original table.
B is the same as the pair (2000, 400) and the second row in the table. C is the same as (2005, 1025) and the third
row in the table; D, the same as (2010, 2009) and the fourth row; and E, the same as (2015, 3225) and the fifth
row.
Applying Function Notation
Examine the following table.
You probably notice a difference between this table and the last one. Rest assured that this one contains the
exact same data, but it is been renumbered to make things a bit easier to deal with. Here, Year 1 represents the
calendar year 1995 and the number of users are expressed in billions, not millions. (To convert into billions,
simply divide the usage numbers in millions by 1000.)
To apply function notation to this data, assign Year as the input variable to the function f. The function f has an
output variable, notated f(YEAR), which in this case is the number of internet users (in billions). Each
output f(YEAR) must be a single value paired to each input. The input variable Year is placed inside the pair of
parentheses of f, and does not refer to multiplication. Now you can
write f(YEAR) = Worldwide internet users in billons.
Here is a key point: The data are exactly the same as they were previously in the original table, the ordered
pairs, and the graph. Nothing has changed except the notation of the ordered pairs. It is sometimes very helpful
to rescale a graph, as in the following graph to make it easier to understand.
2
