Complete the following problems on a separate sheet of paper. Practice showing all work!
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1 MATH 700 FINAL EXAM REVIEW INTERMEDIATE ALGEBRA Complete the following problems on a separate sheet of paper. Practice showing all work!. Find all numbers for which the rational epression is not defined...a. Multiply and simplify: y y y y y y..a. Divide and simplify: 9..b. Find the least common multiple of,,..c. Add and simplify if possible:. Subtract and simplify if possible: t t t t 7. Simplify: 8. Solve: 0 y y 9..a..a 7..a 8..7a 9. In very snowy weather Rick drives his four-wheel-drive truck 0 mph faster than Sarah drives her Saturn. While Sarah travels 0 mi, Rick travels 0 mi. Find their speeds. 9..8a 0. Find an equation of variation in which y varies jointly as 0..9e and z and inversely as the square of w, where y = when =, z =, and w =.. The function C( t) 09.t 77.7 can be used to approimate the average cost of tuition for public four-year colleges, where t is the number of years after 000. a. What will the average cost of tuition be in 00? (a). 7.b b. In what year will the average cost of tuition be $8.70? (b). 7.b Page of
2 . Find the domain of 8 f( ). 7.a. For the graph of the function f shown below determine the following: a. f ( ) (a). 7.a b. the domain (b). 7.a c. all -values such that f( ) (c). 7.a d. the range (d). 7.a. Find the slope, y-intercept and -intercept of:. 7.b y 7 slope 7.b y-intercept 7.b -intercept. Determine if y and y9 are parallel, perpendicular, or neither.. 7.d. Find and graph the equation of the line with slope and y-intercept (0, ).. 7.b equation see graph 7.b 7. Find the equation of a line that goes through the point (, ) and is perpendicular to y d 8. True Tone Graphics bought a computer for $,800. The value V(t) of the computer depreciates at a rate of $0 per month. a. Formulate a linear function for the value V(t) of the computer after t months. 8(a). 7.e b. Use your function to determine the value of the computer after 0. months. 8(b). 7.e MATH FINAL EXAM REVIEW PAGE OF
3 9. For f 9, find f, f, f, and f 9. 0.a 0. Rewrite with rational eponents: a. Simplify: 8. 0.d. Use rational eponents to write as a single radical epression.. 0.a. Rationalize the denominator and simplify. Assume that all epressions under radicals represent nonnegative numbers b. Rationalize the denominator and simplify. Assume that all epressions under radicals represent nonnegative numbers. 00a 7. 0.b. Simplify and write the solution with no negative eponents:. 0.b. Add and simplify:. 0.a 7. Solve for : b 8. The diagonal of a square has length 7 ft. Find the length of the side of the square a 9. Simplify: i d 0. Divide and simplify to the form a bi e 7 i 8i MATH FINAL EXAM REVIEW PAGE OF
4 . The Peachtree Plaza in Atlanta, Georgia, is 7 ft tall. Use the equation h t 0t 7 to estimate how long it would take for an object to fall from the top. Round answer to the nearest hundredth of a second. (Hint: What is the value of h at the ground?)..c. Solve by completing the square:..b. Solve using the quadratic formula:..a. Solve for : ( ) 7 ( )..a. Solve for s: V s h..b. Find a quadratic equation, with integer coefficients, whose solutions are and..b 7. Given the equation f ( ) ( ) a) What are the coordinates of the verte? 7 a).c b) What is the equation of the ais of symmetry? 7 b).c c) Is the verte a maimum or minimum point? 7 c).c d) Sketch the equation on the aes below. 7 d) (sketch below).c MATH FINAL EXAM REVIEW PAGE OF
5 For questions 8 through : Match each equation with the appropriate graph below. A) y B) y C) y D) y 8. y 8..b 9. y 9..b 0. log y 0..a. y (.)..b. (.) y..b. y log...a. a) Graph the inverse of the function,,,,,,, b) Is the inverse a function? Write YES or NO. y Determine if f( ) is one-to-one. If it is, find a formula for its inverse. f ( ) ( ) a) See Graph b..a. YES / NO f ( ) =.bc. Find ( f g)( ) and ( g f )( ). ( f g)( ) f ( ) 8, g( ).d ( g f )( ).d 7. Use composition to show that the inverse is correct. 7..e 7 f ( ) f ( ) 7 MATH FINAL EXAM REVIEW PAGE OF
6 8. Epress as a sum of logarithms: log ( ) c a 8..a 9. Write in logarithmic form. / 9..b 0. Epress as a single logarithm: log a log a y log a z 0..d. Epress in terms of logarithms without using eponents. log d yz..d. Solve for...c. Find the logarithm using the change of base formula. log8 Round answer to four decimal places..b. Solve for. log ( ) log..b. Find the amount owed at the end of 8 years if $,00 is borrowed at a rate of.% compounded annually. Use the formula A P( r) t. Round off to two decimal places...7b MATH FINAL EXAM REVIEW PAGE OF
7 MATH 700 FINAL REVIEW ANSWERS INTERMEDIATE ALGEBRA.,... y y 0 ( ) ( ). ( ) ( ). ( t ) t( t )( t ). y ; 7. y 8. a) V( t) 0t 800 ; b) $,7 9.,,, 0. / / 7.. () y. a 9. Sarah 0 mph; Rick 70mph. z 0. y w. a) $809.70; b) 0. all real numbers and. a) ; ;. b) c) -,, ; y y d) m,. parallel 7 0,, 7,0. ( ) ft. 9. i i. 7.0 sec. i. i.., s V h
8 MATH 700 FINAL REVIEW ANSWERS INTERMEDIATE ALGEBRA a) (,) ; b) ; c) minimum; d) graph 8. C 9. A 0. A. B. D. D. a) graph; b) yes. yes; f ( ). ( f g)( ) ; ( g f )( ) 8 7. yes; 8. log log c f f ( ) c a log z log a y. log log y log z $ d d d
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