Name Date Class ,~I ; Domain, Range, and End Behavior Practice and Problem Solving: AlB Describe the interval shown using an inequality, interval notation. 1. -I I ($ I. I I I I I I I -4 -2 Inequality: Set Notation: 0 3:-,)< X of Interval Notation: 2 "IX) 4 set notation, and 2. -I X ~- :, I ($ I I I ! 14 16. Inequality: 18 I~ = _x2 22 ~;t~ 24 Set Notation: ~ j 5<: X"" .2 t-~ E 3) C'o) Interval Notation:Q 5) 2 . + 3: Domain: - 600Q .::. t",J-- set ><: C" I>C Inequality: X I- Set Notationt Interval Notation; I' 28 26 1- :3 ~'x<:'f:1'D S Describe the domain and range of the graph using an inequality, notation, and interval notation. Then describe its end behavior. 3. Graph off(x) I I I I I I • 20 DO E- l. XL"!? -.3 _ ~ 0 00) 60 ) :3 3 -~ Range: Inequality: _(/QL~ ' Set Notation: - f )(~£~ Interval Notation: C~()OI ~ .; -3J f: 33 End Behavior: \ 4s X-"/t><"' t+~X -') I-?'{~)-? -(.).0 - DQI f(IC.) ~-t>Q Draw the graph of the function with its given domain. Then determine the range using interval notation. 4. g(x)=-3x+2 with domain (-1, 2J: "Y'-iT! --,',' -;-"T'-r-"r,lJ . ;-~,.,.--+ -' )1 - -,(-{)H ! -I S 2 _(..1 l i ; Xl 4 . , : -"j" .. ;0 )! I ., .J i •.. 1 ~n... _)("2)+2 ;- [----j.,."~ -'i'---'"'"'-~'- -i'-'-~-:4- t~t~:t~-r*.t.~~r_;_LL.~---i Range:E.4 Original content Copyright@by J ~) Houghton Mifflin Harcourt Additions and changes to the original content are the responsibility of the instructor, Name Da!e Class _ Domain, Range, and End Behavior Practice and Problem Solving: C For Problems 1-2, let fIx} = x2 - 4. 2. Determine the domain and range of f using set notation and interval notation. Then describe its end behavior. 1. Graph the function. 12 ; j X! - ---G R~ } C>O ~ X .::o.Q~ tx;') 00 ') l_u~,?-~4l ~~ __ LA ---G-4) J) A<;, 'i -"';> Q9 ) -Cry) -+~ -) As x ~ - 0>0) fl>C) -:;,~ oc Home A uses 8 gallons of propane per day for heat. Home Buses 5 gallons per day. Both homes begin with propane tanks filled to their maximum Problems 3-6. capacities of 500 gallons. Use this information for 3. Write two linear functions modeling the amount of propane remaining in each tank per day. Then graph both functions on the same coordinate plane. HomeA B(\{) ::500-~X.H~me B: 9()<)~500 - 5X ~ C2 IS'" - , -;': . A 5'0 100 0560 I() !bU,' D 4. Describe the domain and range of each function using interval notation. D: 10 1"2. V; ~I 'OcJ g:_,So;:'7 <'1 «; @,15)6] 5. Write a function that describes th~bined am~of propane Homes A and B have' remaining in their tanks per day. Use the function to solve for x = 50, and interpret the result. . @lX) ~ fOOd - /3)< ' 9 (~)= It) '5 00 - r,X . , + 500. - 'DO 0 =-/.:, ~ _12 ' [0) 7b.~ f "@/ /000] 2 ~ ts I( 3s-o ::po 1Pf, Original content Copyright ~ by Houghton Mifflin Harcourt, Additions and changes 10the original conlent are the responsibility of the instructor, @ -13 ':""J3X ()O -13::'57,.;) -:: I DOD - 6. Write the domain and range of the function found in Problem 5 using , set notati~n. S >< 0 == IDOO I a 0 . Name Date Class Characteristics of Function Graphs Practice 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? / I 4- ) rm',O ( J, 0 ) trrAy (- 3. What are the zeros of the function? r;-J"O) (f,O) 4. What is the domain and range? :'?i~l3J ;p-o] ~ _' ~ I i •• Shelley is studying the relationship b~tween her car's mileage (miles per gallon) and speed (miles per'hour). The table shows the data Shelley found. Use the table for Problems 5-7. 70 40 50 , 60 30 ~~l~~~i,'wlJI~l~~~~!t}~~~~ iM~~tJ;~?triill~~'1:f~'inlftr~~; .".-.v,,,..~.".....,.'.".'., ."".9•..,,,",,.h 34.0 33.5 31.5 5. Make a scatter plot of the data. Then use a calculator to find an equation for the line of best fit. Sketch the line. Equation oflinej-= (Ir~- ~ 32 example of interpolation or extrapolation? Explain. " 28 ~ij14ok-f-ll)h :1i 5< ~5r1Yl .r 24 ~t 6e(~ &o~;n. 20 o 20 40 )),' '_)../7. ..-'\..- ! :FCS'5):: ~q "1 S or qg ) Is the prediction found in Problem 6 an - /\/ -"-I .'--..: - 27.5 6. Use the equation found in Problem 5 to predict the miles per gallon of Shelly's car for a speed of 55 miles per hour. -.lEX t 3q )6b~, 36 29.0 60 Speed (mph) Original content Copyright@by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 6 ) \ -. Name __ ~ Date Class _ _ Characteristics of Function Graphs Practice and Problem Solving: C The table shows values of a polynomial Problems 1-2. function. 1 2. 3 15 12 41 2. Over which intervals is the average rate of change negative? - 1. Over which intervals is the average rate of \ change positive? [2,3"] -013; Use the table for LO c CO)I] 1.] JJ4?-J---- j • A fireworks projectile is launched at 20 meters per second from a GO-meter cliff. The table shows the height, y, in meters the projectile is above a field after x seconds. Use the table for Problems 3-9. [@m~X~~5~~.~~)~~il3 75 7 6 B~l~ff~J(nr~t~T~jf.t;' 0 1 2 4 5 5 80 60 35 0 3. Make a scatter plot of the data. Then use the QuadReg feature on a calculator to find l} function that bestfils the data. Sketch the function. Functio~: ~ = ...6x ~+- ?-&\ +10 0 5. Over what interval is the projectile's height increasing? [0. 1:) 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 this prediction make sense for the problem situation? EXRlain. S ~ Q~:W'\ 60 .s:: .2' 40 ~ ---(7, -=-15) No Sen-se I ~1~ .t,'J.~1-:J~~_t~-'r~j~~J.'~ ,:J . :, 20 . o I 2 ; , i ' , i 4 1 ' ' ! + f I j !X 6 8 - I :;; I 10 Time (sec) 4. What is the m Xim~m . ight of the projectile? 'J.. rO .:R ) Original content Copyright @ by Houghton Mifflin Harcourt. Addilions I and changes to the original content are the responsibility 7 of the instructor.
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