REVIEW SHEET FOR PRE-CALCULUS MIDTERM
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1 . If A, nd B 8, REVIEW SHEET FOR PRE-CALCULUS MIDTERM. For the following figure, wht is the eqution of the line?, write n eqution of the line tht psses through these points.. Given the following lines, which re perpendiculr to ech other? L : y 4 L : y 7 L : y L : y Solve the following inequlity for nd epress the solution set using intervl nottion b. c. d , 4 nd is prllel to the line y 4.. Find n eqution of line tht psses through the point 6. Find n eqution of line tht psses through the point, nd hs slope of Find n eqution of line tht hd n intercept of 4 nd y intercept of. 8. Find n eqution of line tht psses through the points, nd, Find n eqution of line tht psses through, nd is perpendiculr to the line y.. Find n eqution of line tht psses through the points, nd the midpoint of the line segment from,4 to,. For the points A4, nd B 6,. () Find the distnce between the points nd (b) find the coordintes of the midpoint of the line segment AB,7. Find the distnce between the points: A nd B 6,9. Given the following equtions, which ones re liner? ( I) y ( II) y ( III ) y ( IV ) y 4. Grph the solution of the system of inequlities: #-9, Solve the inequlity: y7 y 7. 8 Solve the system of equtions both grphiclly nd lgebriclly:. y7. y y y. y. y = (+) - 4y = -8 y =
2 4. Which of the following grphs represent functions? () (b) (c) (d) (e). Given the functions: f, g 6, h. Find g h f 9 6. Find the inverse of g, (Why is the restriction on the domin necessry?) 7. Consider the grph of f( ). Nme ny symptotes, intercepts, nd describe the end behvior. Problems 8 4: Solve the equtions for the indicted vrible. y z 8., for 9. V b bc c, for b c. Ar rh, for positive r. AP nrp, for P. yd y d, for d., for 4 4. Find the domin & the rnge of the function: f 7. Given: f () Show tht f 6. Simplify 7. Find f h f h f f,, where () f (b) f (b) Find the domin nd the rnge of f (c) where () f (b) f 6 (c) f f 8. Sketch the grph of the function: g 9. Sketch the grph of the function: h Problems 4 4: The grph of the function is given s: Determine the grphs of the following 4. f 4. f f 4. f 44. Find the -intercept nd the y -intercept of the function: y
3 Problems 4 47: Find the inverse of the function, if it eists. 4. f 46. f If f, for wht vlue of does f? y 49. Simplify: y y. Which eqution is represented by the following grph: 47. f () (b) 7 6 (c) 76 (d) 6 7 (e) None 4. If 4 is zero of the function: f k. Find the vlue of k.. Find the reminder when 4 is divided by.. Find the remining roots of 4, if is root. 4. Find polynomil eqution whose roots re:,, nd. Solve: #6-6, Simplify y y The grph of y is symmetric bout () the origin (b) -is (c) y -is (d) the line y #6-68: Write ech of the following epressions in the form of p q c b, where c,, p nd q re rel numbers. 6. b 64. 9b 6. b b 66. b b 67. b 68. b b
4 69. Rtionlize the denomintor: Problems 7-74: Fctor completely 7. Rtionlize the numertor: Problems 7-8: Find ll rel solutions Find the reminder on division of: by 84. Find the reminder on division of: 4 4 by 8. If one solution of the eqution: is. Find ll other solutions. 86. Find ll solutions of: 8. (All solutions re rtionl nd between ) Problems 87-9: Solve the inequlities If 4 f 7 9, then find f 94. If f, then find f h 9. If 6 & y 9 y, find ) 96. Simplify: Simplify: 98. Sketch the grph : y log end behvior. 99. Find the inverse of: f ln 4 symmetry should you epect to see? b) y. Stte domin, rnge. Nme ny intercepts nd symptotes. Describe the Sketch both f() nd f - () on the sme set of es. Wht type of
5 . Simplify:. Solve: 4. Simplify: ln k e. Solve: log log log 4. Write in eponentil form: log7 m log 7. Simplify: log log 4 log 6. Solve: Solve:. Solve: 7. Solve: Solve: log log log 4 4log. Simplify:. Simplify: log log log 4. Simplify: 4 log. Simplify: log 9 log log. Simplify: log 6. Solve: 7. Simplify: log 4 log 8. Simplify: log 8 9. Simplify:. A mnufcturer of tin cns wishes to construct right circulr cylindricl cn of height h cm nd cpcity c cm. Find the inner rdius of the cn. Find the domin of the given function. f 4. f 9. f. #7-: Find f, f, f, nd f t sin. f 6. f 7. f 8. f 9.. Find f cos nd then sketch the grph. Be sure to lbel units on the es. f,,. f,, f ( ) ( 4). f ( ) e 4 f g nd g f, nd stte the domin of the composite functions.. f 4. f g g Clssify ech function s EVEN, ODD or NEITHER. Support your nswer using either the symmetry of the grph or the definitions of even/odd. EVEN: f(-) = f(), ODD: f(-) = -f().. f 6. f f 8. f 9. f sin 4. cos f
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