Transcript Slide 1

9-1 Multiple Representations of Functions
Objectives
Translate between the various representations of functions.
Solve problems by using the various representations of
functions.
Notes: Recreation Application
Janet is rowing across an 80-meter-wide river at a rate of
3 meters per second.
A) Create a table
B) Write an equation (linear, quadratic or
exponential),
C) Graph of the distance that Janet has remaining
before she reaches the other side.
D) When will Janet reach the shore?
Holt Algebra 2
9-1 Multiple Representations of Functions
An amusement park manager
estimates daily profits by
multiplying the number of
tickets sold by 20. This verbal
description is useful, but other
representations of the function
may be more useful.
These different representations can help the manager
set, compare, and predict prices.
Holt Algebra 2
9-1 Multiple Representations of Functions
Example 1: Business Application
Sketch a possible graph to represent the
following.
Ticket sales were good
until a massive power
outage happened on
Saturday that was not
repaired until late Sunday.
The graph will show decreased
sales until Sunday.
Holt Algebra 2
9-1 Multiple Representations of Functions
Example 2A
What if …? Sketch a possible graph to
represent the following.
The weather was
beautiful on Friday
and Saturday, but it
rained all day on
Sunday and Monday.
The graph will show decreased
sales on Sunday and Monday.
Holt Algebra 2
9-1 Multiple Representations of Functions
Example 2B
Sketch a possible graph to represent the
following.
Only of the rides were
running on Friday and
Sunday.
The graph will show decreased
sales on Friday and Sunday.
Holt Algebra 2
9-1 Multiple Representations of Functions
Because each representation of a function
(words, equation, table, or graph) describes
the same relationship, you can often use any
representation to generate the others.
Holt Algebra 2
9-1 Multiple Representations of Functions
Example 3: Using Multiple Representations to Solve
Problems
A hotel manager knows that the number of
rooms that guests will rent depends on the
price. The hotel’s revenue depends on both
the price and the number of rooms rented.
The table shows the hotel’s average nightly
revenue based on room price. Use a graph
and an equation to find the price that the
manager should charge in order to maximize
his revenue.
Holt Algebra 2
9-1 Multiple Representations of Functions
Example 3A Continued
Does the data does appear linear, quadratic or
exponential?
Holt Algebra 2
9-1 Multiple Representations of Functions
Example 3B: Using Multiple Representations to Solve
Problems
An investor buys a property for $100,000.
Experts expect the property to increase in value
by about 6% per year. Use a table, a graph and
an equation to predict the number of years it
will take for the property to be worth more than
$150,000.
Holt Algebra 2
9-1 Multiple Representations of Functions
Example 3B Continued
Make a table for the property. Because you are interested in the
value of the property, make a graph, by using years t as the
independent variable and value as the dependent variable.
Identify as linear, quadratic, or exponential.
Holt Algebra 2
9-1 Multiple Representations of Functions
Review: Example 4A
4A. The graph shows the number of cars in a
high school parking lot on a Saturday,
beginning at 10 A.M. and ending at 8 P.M. Give a
possible interpretation for this graph.
Possible answer: Football
practice goes from 11:00 A.M.
until 1:00 P.M. Families begin
arriving at 4:00 P.M. for a play
that begins at 5:00 P.M. and
ends at 7:00 P.M. After the
play, most people leave.
Holt Algebra 2
9-1 Multiple Representations of Functions
Review
4B. An online computer game company has 10,000 subscribers
paying $8 per month. Their research shows that for every
25-cent reduction in their fee, they will attract another 500
users. Use a table and an equation (linear, quadratic or
exponential) to find the fee that the company should charge
to maximize their revenue.
Holt Algebra 2
9-1 Multiple Representations of Functions
Notes: Recreation Application
Janet is rowing across an 80-meter-wide river at a rate of
3 meters per second.
A) Create a table
B) Write an equation (linear, quadratic or
exponential),
C) Graph of the distance that Janet has remaining
before she reaches the other side.
D) When will Janet reach the shore?
Holt Algebra 2
9-1 Multiple Representations of Functions
Notes
A. Create a table.
Let t be the time in seconds
and d be Janet’s distance, in
meters, from reaching the
shore.
Janet begins at a distance of
80 meters, and the distance
decreases by 3 meters each
second.
Holt Algebra 2
9-1 Multiple Representations of Functions
Notes
B. Write an equation.
Distance
d
Holt Algebra 2
is equal to 80 minus 3 meters per second.
=
80
–
3t
9-1 Multiple Representations of Functions
Notes
D Find the intercepts and graph the equation.
d-intercept:80
Solve for t when d = 0
d = 80 – 3t
0 = 80 – 3t
t = –80 = 26 2
–3
3
2
t-intercept: 26
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Janet will reach the shore after 26 2 seconds.
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Holt Algebra 2