Name Date Class

Domain, Range, and End BehaviorPractice and Problem Solving: AlB

Describe the interval shown using an inequality, set notation, andinterval notation.

~I, ;

1. -I I ($ I I I I I I I I.-4 -2 0 2 4 :,

Inequality: - 3:-,)< "IX) X ~-Set Notation: of X 1- :3~'x<:'f:1'D SInterval Notation: E3) C'o) .

2. -I I ($ I I I ! I I I I I I •14 16. 18 20 22 24 26

Inequality: I~ ~;t~Set Notation: ~ j 5<: X"" .2 t-~Interval Notation:Q 5) 2 t",J--

I'28

Describe the domain and range of the graph using an inequality, setnotation, and interval notation. Then describe its end behavior.

3. Graph off(x) = _x2 + 3: Domain: - 600Q .::. ><: C" I>C

Inequality: -.3 _ ~Set NotationtX I - DO l.XL"!?Interval Notation; E- 00) 60) 0 :3

Range: 3 -~_(/QL~Inequality: ' - ~ .;

Set Notation: f )(~£~ f:33Interval Notation: C~()OI -3J

End Behavior:

\ 4s X-"/t><"' I-?'{~)-? -(.).0t+~X -') - DQI f(IC.) ~-t>QDraw the graph of the function with its given domain. Then determinethe range using interval notation.

-,(-{)H -I S~n...

_)("2)+2 2 4_(..1 l 0

4. g(x)=-3x+2 with domain (-1, 2J:

"Y'-iT!--,',' -;-"T'-r-"r,lJ. ;-~,.,.--+ -') )!

1 - ;- ., I! .J i

i•.. 1; Xl

. ,: -"j" .. ;- -'i'---'"'"'-~'-[----j.,."~ -i'-'-~-:4-

t~t~:t~-r*.t.~~r-_;_LL.~---i

Range:E.4 J ~)

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Name Da!e Class _

Domain, Range, and End BehaviorPractice and Problem Solving: C

For Problems 1-2, let fIx} = x2 - 4.

1. Graph the function. 2. Determine the domain and range of f using setnotation and interval notation. Then describe itsend behavior.

12 ; j X! - C>O ~ X .::o.Q~

---G tx;') 00 ')

R ~ } LA l_u~,?-~4l~~ __---G-4) J)A<;, 'i -"';> Q9 ) -Cry) -) -+~As x ~ - 0>0) fl>C) -:;,~ oc

5'0 A 100-;': .

- ,

6. Write the domain and range of the function found in Problem 5 using, set notati~n. ~

_12 ' [0) 7b.~ f "@/ /000]

Home A uses 8 gallons of propane per day for heat. Home Buses5 gallons per day. Both homes begin with propane tanks filled totheir maximum capacities of 500 gallons. Use this information forProblems 3-6.

3. Write two linear functions modeling the amount of propane remainingin each tank per day. Then graph both functions on the samecoordinate plane.

HomeA B(\{) ::500-~X.H~me B: 9()<)~500 - 5X

~ 0560

C2 IS'" I () !bU,' D4. Describe the domain and range of each function using interval

notation.

D:101"2. <'1 V; ~I 'OcJ«; @,15)6] g:_,So;:'75. Write a function that describes th~bined am~of propane '5 00 - r,X + 500. - S ><

Homes A and B have' remaining in their tanks per day. Use the . , 0 == IDOO -13 I(

function to solve for x = 50, and interpret the result. . 'DO 0 =- ':""J3X@-/.:, ~@lX) ~ fOOd - /3)< ' 9 (~)= It) ()O -13::'57,.;) -:: IDOD - ts 3s-o::po a

1Pf,I 0 .

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2

Name Date Class

Characteristics of Function GraphsPractice and Problem Solving: AlB

Use the graph to answer Problems 1-4.1. On which intervals is the function increasing and

decreasing?,-In

2. What are ttie local ximum and minimum values?

trrAy (- / I 4- )rm',O ( J, 0 )

3. What are the zeros of the function?

r;-J"O) (f,O)

4. What is the domain and range?

~:'?i~l3J_' ~ I ;p-o]i ••

Shelley is studying the relationship b~tween her car's mileage (milesper gallon) and speed (miles per'hour). The table shows the dataShelley found. Use the table for Problems 5-7.

~~l~~~i,'wlJI~l~~~~!t}~~~~30 40 50 60 70,

iM~~tJ;~?triill~~'1:f~'inlftr~~;34.0 33.5 31.5 29.0 27.5.".-.v,,,..~.".....,.'.". '., ."".9•..,,,",,.h

36

~ 32!" 28.r:1i 24

) \

5. Make a scatter plot of the data. Then use 6. Use the equation found in Problem 5 toa calculator to find an equation for the line predict the miles per gallon of Shelly's carof best fit. Sketch the line. for a speed of 55 miles per hour.

Equation oflinej-= -.lEX t 3q)6b~, :FCS'5):: ~q "1 Sor )),'(Ir~- qg ).'--..: - '_)../7. Is the prediction found in Problem 6 an- /\/ -"-I example of interpolation or extrapolation?

..-'\..- Explain.

~ij14ok-f-ll)h 6e(~5<~5r1Yl ~t &o~;n.

20o 20 40 60

Speed (mph)

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6

-.

Name __ ~ Date _ Class _

Characteristics of Function GraphsPractice and Problem Solving: C

2. 3

12 41

1

15

The table shows values of a polynomial function. Use the table forProblems 1-2.

1. Over which intervals is the average rate of- \change positive?

[2,3"]-013; j•

2. Over which intervals is the average rate ofchange negative?

LO c 1.] CO)I]JJ4?-J----

A fireworks projectile is launched at 20 meters per second from aGO-meter cliff. The table shows the height, y, in meters the projectileis above a field after x seconds. Use the table for Problems 3-9.

[@m~X~~5~~.~~)~~il0 1 2 3 4 5

B~l~ff~J(nr~t~T~jf.t;'60 75 80 75 60 35

.:R )I

6. Over what interval is the projectile's height

decreasing? @ J 5]7. Use the equation found in Problem 3 to find

the height after 7 seconds. Does thisprediction make sense for the problemsituation? EXRlain.

Q~:W'\---(7, -=-15) No Sen-se

- I :;;

5. Over what interval is the projectile's height

increasing? [0. 1:)I

o

S 60~.s::.2' 40 .

~ :, ; , i ' ' ! + I20 ~1~..t,'J.~1-:J~~_t~-'r~j~~J.'~,:J

. I ' , i 1 f I j !X I2 4 6 8 10

Time (sec)

4. What is the m Xim~m . ight of the

projectile? 'J.. rO

3. Make a scatter plot of the data. Thenuse the QuadReg feature on acalculator to find l} function that bestfilsthe data. Sketch the function.

Functio~: ~ = ...6x~+- ?-&\ +10 0

Original content Copyright @ by Houghton Mifflin Harcourt. Addilions and changes to the original content are the responsibility of the instructor.

7