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Copyright 2014 Scott Storla
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Data Table
After 3 payments I owed $850. After 4 payments I owed $650 and after 7 payments I owed $50.
Number of payments
Amount owed(Dollars)
3 850
4 650
7 50
Equation200 1450y x 200 1450A p p
Functional notation allows us to discuss functions without the vagueness of English.
6.5 50H A A
Copyright 2014 Scott Storla
The average height in centimeters of a child in the United States can be estimated by adding fifty to the product of the child’s age and six and a half.
Copyright 2014 Scott Storla
Procedure –Building a Two Item Function Using Functional Notation
a) Decide on the two items. Choose a variable to represent the values of each.
b) Decide which variable will represent the domain values and which will represent the range values.
c) On the left side of the equation write the dependent variable outside parentheses and the independent variable inside parentheses.
d) On the right side use operations to show how to find the range value associated with each domain value.
H
Copyright 2014 Scott Storla
The average height in centimeters of a child in the United States can be estimated by adding fifty to the product of the child’s age and six and a half.
Items: Child’s Age, Child’s Height
Domain: Child’s Age
Range: Child’s Height
A 6.5 50A
A
H
Copyright 2014 Scott Storla
The profit a sports club makes washing cars can
be predicted using the function 10 35 . P c c
Using c to represent the number of cars washed and P to represent the profit made fill in the box on the left side and the right side to write the function in functional notation.
v t
Copyright 2014 Scott Storla
t
Using v to represent the current value of a car and t to represent the number of years since the car was purchased fill in the box on the left side and the right side to write the function in functional notation.
Depreciation is the loss in value of an asset over
time. The value of a car that originally cost
$8,500 depends on the number of years since
the car was purchased and can be modeled
using the function 8,500(0.86) .
The diameter of a storm in miles is useful when
predicting the number of hours a storm will last.
The formula 3
0.07 shows the
relationship between the two.
Copyright 2014 Scott Storla
T D D
Using D to represent the diameter of a storm and T to represent the hours to storm will last fill in the box on the left side and the right side to write the function in functional notation.
Copyright 2014 Scott Storla
Given 70 60 find if 320D t t t D t
70 60D t t
700 032 6 t
250 60t
4.17 t
Copyright 2014 Scott Storla
0.04Given 50,000 find if 75,000tA t e t A t
0.0475,000 50,000 te
0.041.5
ln 1.5 0.04
ln 1.5
0.04
10.1366
te
t
t
t
Copyright 2014 Scott Storla
0.04Given 50,000 find 22tA t e A
0.04 2222 50,000A e
0.8822 50,000
22 50,000 2.4109
22 120,544.9853
A e
A
A
Copyright 2014 Scott Storla
The function 6 213A x x estimates the
number of passenger airlines in the United States x years after 1980.
Translate A(12) into English.
Translate A(x) = 100 into English.
Translate, “How many passenger airlines do you expect this year?” into functional notation.
Translate, “What will be the first year the number of passenger airlines will drop to 60?” into functional notation
In English answer the question A(12) asks.
In English answer the question A(x) = 100 asks.
Predict the year the number of airlines will be half that in 1985.
Predict the number of airlines 10 years after there were 200 airlines.
Copyright 2014 Scott Storla
A ball has been dropped from the top of a building. Its height (in feet) after t seconds is given by the
function 216 256H(t ) t .
Translate H(0) into English.
Translate H(t) = 0 into English.
Translate, “What is the height of the ball after 2 seconds?” into functional notation.
Translate, “How long will it take for the ball to be 100 feet above the ground?” into functional notation
In English answer the question H(2) asks.
In English answer the question H(t) = 100 asks.
Predict the height of the ball 1 second after it’s 100 feet above the ground.
Predict the time it takes for the height of the ball to be 42 feet less than it is after 2 seconds.
Copyright 2014 Scott Storla
The function ( ) 10( 60)F s s determines your fine (F) when your speed (s) exceeds 60 mph.
a) If ( ) 95F s find s and discuss its meaning.
b) Find (80) and (50)F F and discuss the meaning of each.
c) Translate the question (110)F is asking into English and use the function to answer the question.
d) Translate the question ( ) 350F s is asking into English and use the function to answer the question.
e) Someone says they had to pay a fine of $500. Translate their situation into functional notation and find their speed
Copyright 2014 Scott Storla
The number of people N at a reception t hours after the
reception starts can be modeled using the function
225 2 100N(t ) (t ) . Assume the reception starts at 8 p.m.
a) In English explain what 400N(t ) is asking and use the
function to answer the question.
b) Find 4N( )and discuss its meaning.
c) Translate, “How many people will be attending the reception at 11:30?” into functional notation and use the function to answer the question.
d) Translate, “When will there be 125 people at the reception?” into functional notation and use the function to answer the question.
Copyright 2014 Scott Storla
The function 0.012( ) 240,000 tP t e describes the
population of a city t years after 2005.
Translate P(0) into English.
Translate P(t) = 210,000 into English.
Translate, “What will the population be in 2017?” into functional notation.
Translate, “What year will the population reach 185,000?” into functional notation
In English answer the question P(-1) asks.
In English answer the question P(t) = 210,000 asks.
Predict the height of the ball 1 second after it’s 100 feet above the ground.
Predict the time it takes for the height of the ball to be 42 feet less than it is after 2 seconds.
Copyright 2014 Scott Storla
The function 2( ) 0.3( 1.3) 3P t t approximates the percent of people
using online banking in the United States t years after 1995. (Caution, 90% would be 90 not 0.9.)
a) Translate the sentence, “Estimate the first year at least seventy percent of households will be using online banking.” To functional notation and use the function to answer the question.
b) Translate the sentence, “What percent of people were using online banking in two thousand seven?” to functional notation and use the function to answer the question.
c) Translate the question ( 1)P is asking into English and use the function to answer the question.
d) Translate the question ( ) 41P t is asking into English and use the function to answer the question.