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Section exercises

Verbal

Terry is skiing down a steep hill. Terry's elevation, E ( t ) , in feet after t seconds is given by E ( t ) = 3000 70 t . Write a complete sentence describing Terry’s starting elevation and how it is changing over time.

Terry starts at an elevation of 3000 feet and descends 70 feet per second.

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Maria is climbing a mountain. Maria's elevation, E ( t ) , in feet after t minutes is given by E ( t ) = 1200 + 40 t . Write a complete sentence describing Maria’s starting elevation and how it is changing over time.

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Jessica is walking home from a friend’s house. After 2 minutes she is 1.4 miles from home. Twelve minutes after leaving, she is 0.9 miles from home. What is her rate in miles per hour?

3 miles per hour

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Sonya is currently 10 miles from home and is walking farther away at 2 miles per hour. Write an equation for her distance from home t hours from now.

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A boat is 100 miles away from the marina, sailing directly toward it at 10 miles per hour. Write an equation for the distance of the boat from the marina after t hours.

d ( t ) = 100 10 t

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Timmy goes to the fair with $40. Each ride costs $2. How much money will he have left after riding n rides?

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Algebraic

For the following exercises, determine whether the equation of the curve can be written as a linear function.

2 x 2 + 3 y 2 = 6

No.

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For the following exercises, determine whether each function is increasing or decreasing.

f ( x ) = 4 x + 3

Increasing.

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a ( x ) = 5 2 x

Decreasing.

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h ( x ) = 2 x + 4

Decreasing.

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j ( x ) = 1 2 x 3

Increasing.

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n ( x ) = 1 3 x 2

Decreasing.

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For the following exercises, find the slope of the line that passes through the two given points.

( 2 ,   4 ) and ( 4 ,  10 )

3

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( 1 ,  5 ) and ( 4 ,  11 )

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( −1 , 4 ) and ( 5 , 2 )

1 3

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( 8 , −2 ) and ( 4 , 6 )

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( 6 ,   11 ) and ( 4 ,   3 )

4 5

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For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

f ( 5 ) = 4 , and f ( 5 ) = 2

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f ( −1 ) = 4 and f ( 5 ) = 1

f ( x ) = 1 2 x + 7 2

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( 2 , 4 ) and ( 4 , 10 )

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Passes through ( 1 , 5 ) and ( 4 , 11 )

y = 2 x + 3

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Passes through ( 1 ,  4 ) and ( 5 ,  2 )

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Passes through ( 2 ,  8 ) and ( 4 ,  6 )

y = 1 3 x + 22 3

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x intercept at ( 2 ,  0 ) and y intercept at ( 0 , −3 )

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x intercept at ( 5 ,  0 ) and y intercept at ( 0 ,  4 )

y = 4 5 x + 4

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Graphical

For the following exercises, find the slope of the lines graphed.

For the following exercises, write an equation for the lines graphed.

Numeric

For the following exercises, which of the tables could represent a linear function? For each that could be linear, find a linear equation that models the data.

x 0 5 10 15
g ( x ) 5 –10 –25 –40

Linear, g ( x ) = 3 x + 5

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x 0 5 10 15
h ( x ) 5 30 105 230
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x 0 5 10 15
f ( x ) –5 20 45 70

Linear, f ( x ) = 5 x 5

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x 5 10 20 25
k ( x ) 28 13 58 73
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x 0 2 4 6
g ( x ) 6 –19 –44 –69

Linear, g ( x ) = 25 2 x + 6

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x 2 4 6 8
f ( x ) –4 16 36 56
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x 2 4 6 8
f ( x ) –4 16 36 56

Linear, f ( x ) = 10 x 24

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x 0 2 6 8
k ( x ) 6 31 106 231
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Technology

If f is a linear function, f ( 0.1 ) = 11.5 ,    and   f ( 0.4 ) = 5.9 , find an equation for the function.

f ( x ) = 58 x + 17.3

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Graph the function f on a domain of [ 10 ,   10 ] :   f ( x ) = 0.02 x 0.01. Enter the function in a graphing utility. For the viewing window, set the minimum value of x to be 10 and the maximum value of x to be 10.

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Graph the function f on a domain of [ 10 ,   10 ] : f x ) = 2 , 500 x + 4 , 000

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Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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