1310 review test4(new) - uh

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MATH 1310 Review for Test -4 Where: CASA Testing Center Time: 50 minutes Number of questions: ?? ? Multiple Choice Questions (total of ?? pts ) ? Free Response Question (total of ?? pts) What is covered: Chapter 4, Sections 5.1 – 5.3 Do not forget to reserve a seat for Test – 4! Take practice Test – 4! 10% of your best score will be added to your test grade at the end of the semester. For the free response part, please show your work neatly. Do not skip steps. Remember the make-up policy: No make-ups! 1) Find the y-intercept of the function

a) 22 )2)(54()( xxxxf

b) xxxxf 86)( 23

2) Find the zeros of the polynomial: )82()6()( 23 xxxxP

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3) Find the zeroes (may be complex) of the polynomial

a) 64)( 2 xxP

b) 80165)( 23 xxxxf 4) Find a 3rd degree polynomial with integer coefficients with zeroes 5 and i2 , and constant coefficient 40.

5) Find the quotient and remainder: 5

143

x

xx

3

6) Find the quotient and remainder: 27

6167 2

x

xx

7) Find the x- and y-intercepts of the function 1

5)(

2

x

xxf

8) Given the following function, find any holes, vertical asymptotes, horizontal asymptotes.

a) 2

2

10 25( )

6 5

x xf x

x x

b) 4

82)(

2

x

xxxf

c) 2

2

2( )

9 36

x xf x

x

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9) Graph the function )3()2()( 2 xxxP . On your graph: Clearly label the x-intercept(s) and y-intercept. Show the correct end behavior and the correct behavior at each x-intercept.

10) Graph the function 2

4)(

x

xxf .

State the x-intercept(s), y-intercept, horizontal asymptote, vertical asymptote(s) and holes and clearly show these features on your graph.

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Exercise: Graph the following functions:

2( ) ( 4) ( 3)P x x x . On your graph: Clearly label the x-intercept(s) and y-intercept. Show the correct end behavior and the correct behavior at each x-intercept.

1( )

3

xf x

x

.

State the x-intercept(s), y-intercept, horizontal asymptote, vertical asymptote(s) and holes and clearly show these features on your graph.

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11) Evaluate the logarithmic function if it is defined. If not defined, say undefined.

)27(log3

)6(log 76

ln(32)e

2

1log ( )

16

ln( 2)

16log 1

12) Find the value of x given that a) 0)(log7 x

b) 1)(log4 x c) 4)(log2 x d) 2)2(log5 x

13) Find the domain and range of a) 9)(log)( 2 xxf b) )42(log)( 5 xxf

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14) Solve for x, given that

a) 72 x

b) 54 1 x

15) Given the function 45)( 2 xxg , find Domain_____________ Range _____________ y-intercept ___________ Asymptote ____________ New Key Point – Shifted (0,1) ______________ 16) Write the exponential function of the form ( ) xf x a which passes through the points (0,1) and (3,64).

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17) Write the exponential function whose graph is given below:

A) 62 1 x

B) 62 1 x

C) 62 1 x

D) 12 6 x

E) 12 6 x 18) Write in logarithmic form:

3662

25 x 19) Write in exponential form: 2)(log3 x

20) Write the following logarithm as a sum of logarithms with no products, powers or quotients.

)4()1(

)2(ln

3

2

xx

xx

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21) Write the following expressions as a single logarithm:

)1ln(5)ln(2 xx

Math 1310 Section 5.4

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Math1310Section5.4:PropertiesofLogarithmsYouwillsometimesbeaskedtorewritelogarithmicexpressionsineitheranexpandedorcontractedform.Todothis,youwillusetheLawsofLogarithms.Youmustknowall8oftheLawsofLogarithms.LawsofLogarithmsIfm,nandaarepositivenumbers,a≠1,then1. log log log 2. log log log 3. log log 4. log 1 05. log 16. log 7. 8. log

changeofbasesformula

Thesepropertiesaretrueforlogsofanybase,includingcommonlogsandnaturallogs.Example1:Rewriteeachofthefollowingexpressionsinaformthathasnologarithmsofaproduct,quotientorpower.

a.log3

b.ln

Math 1310 Section 5.4

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c.log4

d.log

e. ln√ 42 5

f. log1 2

2

Math 1310 Section 5.4

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Question 3. Expand: lnx

yz

a. ln x – ln y + ln z b. ln x – ln y – ln z c. ln x + ln y + ln z d. none of these

Example2:Expresseachasasinglelogarithm:a. log – 3 log

b.2 ln 3 ln 2 – 5 ln

c.12ln 2 3 ln 1

d. 2 log 5 log 1 2log 1

Math 1310 Section 5.4

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e. ln 18 ln 2Example3:Rewriteeachassumssothateachlogarithmcontainsaprimenumber.a. ln 72b. log 96

Example4:Usethechangeofbasesformulatosolvelog 12 andwriteinsimplestform.

Math 1310 Section 5.4

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Example5:Simplifyeach.a. log 16 b.7