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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

the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
what is cell divisoin?
Aron Reply
Diversity of living thing
ISCONT
what is cell division
Aron Reply
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
What is life?
Allison Reply
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
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Practice Key Terms 7

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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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