Precalculus Final Exam Version A Part 1 You may write on this test Name Date Period 2016 Flamingo MathTM Jean Adams 2016 Flamingo MathTM Jean Adams Pre Calculus Final Examination Form A No Calculator allowed on this part of the exam Work each question carefully on separate paper Then choose the letter that corresponds to the best answer and bubble your choice on the scantron provided 1 State the transformations that have occurred to create the function 2 x f x 3 from the function 5 g x 3 x A The graph of the function has been stretched horizontally and shifted up five units B The graph of the function has been stretched vertically and shifted up five units C The graph of the function has been stretched horizontally and shifted down five units D The graph of the function has been stretched vertically and shifted down five units 2 What is the range of the function 4 2 f x x 3 2 A 4 C 4 3 Find the inverse function of g x 3 x 7 A g 1 x 3 x 7 C g 1 x 3 x 7 B 4 D B g 1 x 3 x 7 D 1 x g x 3 37 2016 Flamingo MathTM Jean Adams 4 Find the composition f g x given f x x 2 g x 8 x 6 A f g x 2 2 x 1 B f g x 8 x 2 6 C f g x 8 x 4 D f g x 2 2 x 1 5 Rewrite the expression as a single logarithm 7ln xy 5ln yz 6 What value of x satisfies the equation log 2 5 x 1 2 sec and is in Quadrant IV 7 2 A ln 7 ln 5 xy yz C ln 7 x 5 z A 13 C 5 5 7 Find tan given A 3 5 2 C 7 2 B 7 2 ln x y z 5 D ln ln 7 7 x y 5 5 y z B 12 D 4 5 B 3 5 D 3 5 7 2016 Flamingo MathTM Jean Adams 8 Factor and simplify 2 cos x 2 sin x 2 cos x 9 Which expression completes the Pythagorean Identity for 2 tan 10 Find the exact value of the expression 1 1 cos sin 2 B 4cos x D 1 sin x 2 B 2csc 1 D 2sec 1 B 3 2 D 0 A 2cosx C 4cos x A 1 sec 2 C 1 csc 2 A 2 2 C 1 11 What are the polar coordinates of the point 6 2 3 where 0 360 A 4 3 60 and 4 3 300 B 4 3 120 and 4 3 240 C 4 3 150 and 4 3 330 D 4 3 30 and 4 3 330 2016 Flamingo MathTM Jean Adams 12 Write the complex number in standard form 8 cos30 i sin30 A 4 3 4i C 1 4 3 4 i 13 Find the product 1 B 4 4 3i D 3 4 1 i 4 z z 2 where z 1 3 cos55 i sin55 and z 2 2 cos20 i sin20 A 3 2 cos 35 i sin 35 B 3 2 cos 75 i sin 75 C 3 2 cos 75 i sin 75 D 3 2 cos 1100 i sin 1100 14 Use DeMoivre s Theorem to find 2 cos30 i sin30 5 A 16 3 16i C 16 16 3i B 32i D 32 15 Find an equation for the parabola with vertex at the origin and directrix x 12 A x 2 48 y C y 2 48 x B x 2 48 y D y 2 48 x 2016 Flamingo MathTM Jean Adams 16 Find an explicit rule for the nth term of the sequence 5 15 45 135 A 3 5 n f n C f n 5 3 n B 3 5 n f n 1 D f n 5 3 n 1 17 Use the piecewise function shown at right to find the limit lim f x 2 x A 3 B 3 5 C 4 lim f x 1 x A 2 B 1 C 0 D Does not exist 18 Use the piecewise function at right to find the limit D Does not exist 2016 Flamingo MathTM Jean Adams 19 Find the limit lim 3 x 2 x x 2 x 3 15 A 8 C 0 A 6x C 3 2x B 5 D Does not exist B 6 2x D 6 2x x h 20 Find the derivative of the function 3 f x x 2 2 x by finding f x h h lim 0 h f x 2016 Flamingo MathTM Jean Adams