functional notation copyright 2014 scott storla. written graph data table number of payments amount...

Functional Notation

Copyright 2014 Scott Storla


Written

Graph

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


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.


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


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


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


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.


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.

Using functional notation



Given the function 70 60 find 4D t t D

70 60D t t

70 04 6 4D

4 310D


Given 70 60 find if 320D t t t D t

70 60D t t

700 032 6 t

250 60t

4.17 t


Given 3 7 4 find 2A x x A

2 23 7 4A

2 3 3 4A

2 5A


Given 3 7 4 find if 2A x x x A x

2 3 7 4x

6 3 7

2 7

4 7

3

x

x

x

x


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


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

NextUsing functional notation to ask and answer questions


Applying functional notation



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.


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.


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


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.


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.


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.

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