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Algebra2/Trig

Chapter3review…goodforFRQ

Name:________________________________

Date:______________________Per:_______

1.)Graphthefollowingsystemofinequalities:.

1< 2 x +1 ≤ 5

 y < 2 x +1 + 3Labelimportantpointsandgraphasneatly

aspossible,showsolutionareaclearly.

2.)Graphthefollowinginequality: y < 2 x − 7 +1 .Graph

neatly,labelimportantpointsandshowthesolutionarea

clearly.

3.)Youwanttoburn380caloriesduring40minutes

ofexercise.Youburnabout8caloriesperminute

inlineskatingand12caloriesperminuteswimming.

Howlongshouldyouspenddoingeachactivity?

4.)Graphtheinequalitiesbelow.Showallworkclearlyand

neatly.Labelimportantpoints.Showsolutionareaclearly.

5.)Solveusingeliminationorsubstitutionmethod.Leave

answersinsimplestfractionalform.

6.)Findtheequationofthelineinstandardformthrough

thefollowingtwopoints.

;

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7.)Solveforkgiventhefollowinginformation.

8.)Solveforkgiventhefollowinginformation.

9.)Findanequationinf(x)=mx+bformforthelinear

function.

f(‐1)=3;f(3)=1

10.)Findanequationinstandardformfortheline

described,through(‐3,2)andparalleltotheline

containing(2,3)and(1,‐2)

11.)Findvaluesforcandd sothefollowingsystemof

equationshasaninfinitenumberofsolutionsfor(  x,y ):

5 x + 6 y = 4

2 x − cy = d 

12)Givenconstantsa,b,c,andd ,solvefor( x,y ):

13)Findthevalueofk suchthatthelinethrough P(k -6, 5+k ) and Q(k +4, 3-k ) hasaslopeofk.Thenwritethe

equationofthelineinpointslopeform

14)Solvethesystemofequations

and

15)Dotheaboveproblemagainifinsteadofxitisx‐4andinsteadofyitisy+2

16.)WhatisthepointthatistheSHORTESTdistancefrom(‐3,7)totheliney=‐.5x+6?

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16)Usetheequationsinproblem8tocompletethefollowing:

Find f (a+h)− f (a−h)

2h

Find−2 f ( x + 3)− 4(2g( x))

3 x +1….

Find  f (−2g( x + h))

Findtheslopeofthelinebetween (a, f (a)) and (a, f (a + h))

 

Find the indicated values.

1. Given  f ( x) = 3 x2+ 5, find f (4).  

2. Given  f ( x) = 5 x3+ 3 x2, find f (!3). 

3. Given  f ( x) = 5 x2+ 3 x, find f ( x + h).  

4. Given  f ( x) = 21 x2! 20 x, find f ( x + h). 

5. Given  f ( x) = 3 x2+ 5 x and g( x) = 7 x + 3, find f ( x)g( x). 

6. Given  f ( x) = 6 x3+ 7 and g( x) = e x , find f ( x)g( x).  

7. Given  f ( x) = 3 x2+ 4 x + 5 and g( x) = x2

+ x +1, find f ( x)g( x) if x = 3. 

8. Given  f ( x) = 2 x2+ 5 x and g( x) = 3 x, find f (g( x)). 

9. Given  f ( x) = 2 x2+ 5 x and g( x) = 3 x, find g( f ( x)). 

10. Given g( x) = 5 x2

+ 5 x + 5 and h( x) = 4 x + 4, find g(h( x)). 

11. Given g( x) = 5 x2+ 5 x + 5 and h( x) = 4 x + 4, find h(g( x)). 

12. Given h( x) = 16 ! 35 x , find h(2).  

13. Given  f ( x) = 5 ! 23 x , find f (3).  

14. Given  f ( x) = e x !and! g( x) = 3 x2+ 2 x + 6, find f (g( x)). 

15. Given  f ( x) = e x and g( x) = 3 x2+ 2 x + 6, find g( f ( x)). 

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 y

 x

4

4 –4

 –4

 y

 x

4

4 –4

 –4

 y

 x

4

4

 –4

 –4

For each graph given in parts (a) through (c), describe the domain and range.

a. b. c.

d. If   f ( x) = 3! x2 , calculate  f (5)  and  f (3a) . 

e. If g( x) = 5 ! 3 x2 , calculate g(!2) and g(a + 2) .

f. If   f ( x) = x+32 x!5

, calculate  f (2) and  f (2.5) .

g. If   f ( x) = x2+ 5 x + 6 , solve  f ( x) = 0 . 

h. If g( x) = 3( x ! 5)2 , solve g( x) = 27 .

i. If   f ( x) = ( x + 2)2 , solve  f ( x) = 27 .

! "   !  

! "  

> !  

=   = !  

! = !   + = ! ! !  

= !  

= !   = !  

=   =  

= ! ±