Pre-Calculus B Semester 1 Review Packet December 2015

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Dwayne Stevenson
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1 Pre-Calculus B Semester Review Packet December 05 Name DISCLAIMER The memor on all calculators will be cleared the da of the final. If ou have programs on our calculator that ou would like to keep, please plan accordingl. I. Graphing : Graph the following equations as accuratel as ou can. List at least points for each graph. + =. 5. ( ) = ( + ) = 5 4. = ( 4) = + 6. = [ ] = + 8. this is the greatest integer function + 5 = + 9. = +

2 = log ( ). 0. = ln + 6. f + ( ) = + if if if < 0 = 0 > f( ) = 9 4. g ( ) = h ( ) = + 6. k ( ) = m ( ) = ( 4)( + + )( )

8. Find the center and radius of the following circles: A. + 6 + 8 = 0 B. + +6 + 8 = 0 II. Functions. Are the following equations smmetric with respect to the -ais, -ais, and/or the origin?

3 8. Find the center and radius of the following circles: A = 0 B = 0 II. Functions. Are the following equations smmetric with respect to the -ais, -ais, and/or the origin? Also, classif each of the following equations as even, odd or neither. Justif our answer algebraicall. A. = B. 5 = 6 C. = 9. Answer the following questions about the graph of g() below: G() A. G( ) = B. Find the domain of G ( ) C. Find the range of G ( ) D. List the intervals on which G ( ) is increasing E. Is G (4) positive or negative? F. If G ( ) even, odd or neither? G. What is the minimum value of G ( )? The maimum?. Answer the following questions about the graph below: A. Domain: B. Range: C. Minimum: D. Maimum E. Intervals graph is increasing and decreasing:

4 4. Find the domain and range of each of the following. A. {(0,5),( 7,6),(,8) } B. + 5 = C. = + D. 4 = + ( ) 6 5. Find the inverse of each function, or A. f() = {(,0),(,8),(4,) } B. f ( ), if possible. State the domain and range of both f () and f ( ). + f( ) = ( + ) C. f( ) = D. f( ) = Suppose Find : f( ) =, h ( ) =, A. ( f + g)() B. ( g j)() j ( ) = and ( ) g is given b f h C. ( 5) ( ) g D. ( h j)(7) E. f ( 7) F. g () G. the range of f( ) H. [ go f](0) I. [ f o g]( 4) J. j(h()) K. Find the domain of j(h()) 7. Given f ( + h) f () h, evaluate the difference quotient for f () = 5 +.

5 III. Quadratic Functions Sketch a graph and find the verte, ais of smmetr, -intercepts, -intercepts for each quadratic function.. = 6+. = David has available 400 ards of fencing and wishes to enclose a rectangular area. Do not use a graphing calculator!!! A. Epress the area A of the rectangle as a function of the width of the rectangle. B. For what value of is the area largest? 4. A right triangle has one verte on the graph of = 9 where > 0, at (, ) positive -ais at (,0). Epress the area A of the triangle as a function of., another at the origin, and the third on the

6 IV. Solve the following equations. Show all work.. ( ) = 6. (6 ) ( + ) = 6. + = = = 6. 5= = ( + ) +6 = = = = 0. ( ) V. Solve the following inequalities. Write answers in interval notation.. 5< < 5. < > ( + )( 4) < 0 8 5

7 VI. Polnomials. Write the equation in EXPANDED polnomial form if the degree of the polnomial is 4 and the zeros are: 7i, with multiplicit of.. Write each polnomial in factored form. Find the real and comple roots. Sketch a graph on the aes provided. A. 4 f( ) = B. f( ) = C. f 4 ( ) =

8 VII. Simpl the following without using a calculator.. log. log. log5 8 5 log ln e 6. log6 6 VIII. Epand or condense the following logarithmic epressions. Simplif if possible. 4. log5 log5 + log5. log a 9 log a. [log( + ) + log( )] log 5 4. ln 5z 5. log 9 + IX. Solve each of the following. Round to the nearest tenth if necessar.. 8 = =. log 64( ) ln + ln = ln log + log ( + ) = 5. ln(ln( e )) = e = 6 ln

9 = = = = 7 +. e e 6 0 =. 4 0 =. Solve for in terms of : 5 = e X. Eponential/Logarithmic Applications. In 000, the population of Israel was approimatel 6.04 million and b 050 it is projected to grow to 0 million. a. Write an equation, using the form A = A 0 e kt, in which t is the number of ears after 000, to find an eponential growth function that models the data. b. In which ear will Israel s population be 9 million?. The half-life of the radioactive element krpton-9 is 0 seconds. If 6 grams of krpton-9 are initiall present, how man grams are present after 0 seconds? After 0 seconds? 0 seconds? T seconds?. A bird species is in danger of etinction and has a population that is decreasing eponentiall. Five ears ago, the population was at 400 and toda onl 000 of the birds remain. Once the population drops below 00, the situation will be irreversible. When will this happen?

10 4. A bottle of juice initiall has a temperature of 70 o F. It is left to cool in a refrigerator that has a temperature of 45 o F. After 0 minutes, the temperature of the juice is 55 o F. A. Use Newton s Law of Cooling ( u(t) = T + ( u 0 T )e kt ) to find a model for the temperature of the juice, u, after t minutes. B. What is the temperature of the juice after 5 minutes? C. When will the temperature of the juice be 50 o F? 5. You have $0,000 to invest. One bank pas 5% interest compounded quarterl and the other pas 4.5% interest compounded monthl. Which bank will offer a better value for our mone after ears? 6. Find the accumulated value of an investment of $0,000 for 5 ears at an interest rate of 5.5% if the mone is compounded semiannuall? Quarterl? Continuousl? 7. What is the interest rate if a $4000 investment becomes $47 after ears when compounded dail? (no leap ears)

MATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1)

MATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1) MATH : Final Eam Review Can ou find the distance between two points and the midpoint of a line segment? (.) () Consider the points A (,) and ( 6, ) B. (a) Find the distance between A and B. (b) Find the