MATH 109 SAMPLE FINAL EXAM SPRING 2016

Transcription

1 MATH 09 SAMPLE FINAL EXAM SPRING 0. Find an equation of the line, passing through the point (, ), whose graph is parallel to the graph of the line passing through (-, -) and (, ). a) y b) y c) y (/ ) d) y (/ ). Find the equation of the line, passing through the point (, ), whose graph is perpendicular to the graph of the line passing through (-, -) and (, ). a) y b) y c) y (/ ) d) y (/ ). If the graph of y f () is then the graph of y f ( ) is a) b) c) d) 4. If f ( ) and g( ), then ( g f )( ) equals a) b) c) d). If, then equals

2 a) b) c) d) log (). The real zeros (roots) of the polynomial function p( ) ( 9)( )( ) are a), b),,, c),, i,i d), 7. The domain, D, and range, R, of the function y f ( ) log ( 7) are 9 a) D 7, R y y 7 b) D 7, R all real numbers c) D 7, R all real numbers d) D 7, R all positive real numbers 8. If p( ) pare () a),, 4 4 c),, 4, then the verte and ais of symmetry of the graph of b),, d) 4,, The cost in dollars of removing p percent of the air pollutants in the stack emissions of a utility company that burns coal to generate electricity is given by If the company attempts to remove 00 % of the pollutants the cost will a) increase without bound. b) be $ p C( p) 00 p c) be $ d) be undetermined from the information given. 0. If f ( ) then the inverse function of f( ) is. a) c) f ( ) f ( ) b) d) f ( ) f ( )

3 . The graph of the polynomial function p () n a n... a a 0 may look similar to the given graph if a) an 0 and n is even. b) an 0 and n is odd. c) an 0 and n is even d) an 0 and n is odd.. The horizontal asymptote(s) of the graph of a) y 4, y b) 4, y d) 4, c) f() 0 is (are). A relatively small lake in northern Wisconsin has had all fish removed. Now the DNR will stock it with trout. The number of trout, F, in thousands, after weeks is modeled by F ( ) 0( ). The carrying capacity of the lake is. a) about 000. b) about c) about d) unlimited. 4. The circle whose equation is given by given by y 8 y 0 has center and radius a) Center = (-4, ), Radius = b) Center = (4, -), Radius = c) Center = (-4, ), Radius = d) Center = (4, -), Radius =. If log( ) log ( 4) then equals a) -7 or b) -7 c) 7 or - d). Building supply company A charges $.00 plus $0.00 per hour to rent an insulation blower while company B charges $4.00 plus $8. per hour. How many

4 4 hours and minutes (to the nearest minute) must one rent from company B to have as good a deal as a company A rental? a) hr. b) 4 hr. and 49 min. c) 4 hr. and 0 min. d) 4 hr. and 48 min. 7. A P r nt n Katrina invests $4.00 in a CD paying.4 % compounded monthly for five years. After five years, the amount she will have in the account is a) $09.77 b) $07.79 c) $49. d) $ If a) f ( a h) f ( a) f ( ) then h ah h h b) a c) a h d) ah h 9. The graphs of f( ) and g ( ) are shown in the following figure. Which of the following pair of functions best define f( ) and g ( )? a) f ( ), 0 and g () b) f ( ) ( ), and g( ) c) f( ) and g ( ) log d) f ( ) ( ), and g () 0. Given that ( ) f is a one-to-one function and a a) b) 4 c) 8 d). The domain of f ( ) log 8(4 ) in interval form is a) (0, ) b), 4 c) (, ) f a, the value of f (4) is d) [, )

5 . The vertical asymptote(s) of the graph of a) y 4, y b) 4, y d) 4, c) f() 0 is (are). If f( ) is an even function then its graph is symmetrical with respect to a) the origin. b) the -ais. c) the graph of the line y. d) the y-ais. 4. A catapult launches a boulder vertically into the air. The boulder s height is determined by s( t) t t. The maimum height reached by the boulder is a) ft. b) ft. c) 04 ft. d) ft.. The vertical asymptote of the graph of ylog ( ) is a) b) c) y d) y.the deer population P, in thousands, of Hunting county is projected to be 0.0t P e where t is the number of years from the present. If this projection is correct, then the length of time it will take for the deer population of Hunting county to double its present value is a) ln years b) ln ln years c) ln 0.0 years d) ln 4 0.0ln years 7. Given f ( ) log and g ( ). Which of the following if correct information about the graphs of function f and g : a) f is increasing and g is decreasing b) f is increasing and g is increasing c) f is decreasing and g is decreasing d) f is decreasing and g is increasing 8.Solve the equation 0 given that is a zero of f ( ), the other zeros are a), b), c), d), 9. The solution for the inequality in interval notation is

6 a) [,] b) [, ] c) [,] d) (, ] [, ) 0. The solution for the inequality 4 in interval notation is a) (, ] [, ) b) ANSWERS (, ] [, ) c). B 4. A 7. D. D. D 8. D. C. B 9. C 4. B 7. A 0. B. A 8. C. D 9. B 7. C 0. D 8. B. B 9. A. B 0. D. D. B 4. C. C. B. B. C [, ] d) [,] Good Luck with Your Finals!