15. Let f (x) = 3x Suppose rx 2 + sx + t = 0 where r 0. Then x = 24. Solve 5x 25 < 20 for x. 26. Let y = 7x

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1 Pretest Review The pretest will onsist of 0 problems, eh of whih is similr to one of the following 49 problems If you n do problems like these 49 listed below, you will hve no problem with the pretest Vlues of trig funtions t referene ngles Find os ( Find s ( 5 Find sin ( π) 4 Find tn ( 5 Find se ( 7 6 Find ot ( 4 π) Trig identities 7 Give the formul for os (x y) in terms of os x, 8 Give the formul for os (x) in terms of os x nd sin x 9 Give the formul for os (x + y) in terms of os x, 0 Give the formul for sin (x y) in terms of os x, Give the formul for sin (x + y) in terms of os x, Give the formul for sin (x) in terms of os x, sin x Lw of osines nd sines In the piture, θ = 4 π, α = π nd = Find α b θ β 4 In the piture, = 5, b =, nd θ = 6π Find b θ Inverses 5 Let f (x) = x 7 x+5 Find f (x) 6 Suppose rx + sx + t = 0 where r 0 Then x = 7 Find ll solutions to x 4 x + 0 = 0 8 Find ll solutions to x + 5x + 6 = 0 9 Suppose x + y = 4 nd x 4y = 4 Find x y 0 For wht vlue of k does the system of equtions, x + y =, x + ky = hve no solution? Word problems A wter tnk is initilly 4 full After dding 4 gllons of wter, it is 7 8 full Wht is the pity of the tnk in gllons? The perimeter of retngle is 9 times its width If the length of the retngle is 49, find its width Solving inequlities Solve x (x + 5) (x 4) < 0 for x 4 Solve 5x 5 < 0 for x 5 Find the solution to the inequlity, 4x < 6 Solving Equtions 6 Let y = 7x+5 x 7 Solve for x 7 Solve for x in the eqution 0 ( + 7x) / + 85x ( + 7x) / = 0 8 Find ll positive solutions to (x + 6) = 6 Simplifying expressions 9 Simplify ( 4 ) 4 0 Simplify xy xy Simplifying Simplify x +4 + x Simplify x 4 + x 6 Simplify Simplify Simplify differene quotient 5 Suppose f (x) = x + 6x Simplify f(x+h) f(x) h Ftoring of polynomils 6 Ftor the polynomil x + x Ftor the polynomil 6x + 4x + 4

2 Composition Of Funtions 8 Suppose f ( ) =, f () =, nd f () = while g () =, g ( ) =, nd g () = Find f (g ( + )) 9 Let f (x) = x + x nd let g (x) = x Find f (g ()) Lines 40 A line hving the eqution y = mx+b psses through the points ( 4, 7) nd (9, ) Find m + b 4 Find the eqution of the line through the points ( 4, ), (5, 4) 4 Find the eqution of the line perpendiulr to 8x+ 6y = 6 through (0, 6) 4 Find the eqution of the line prllel to x + y = nd pssing through (0, 8) 44 A line hs the eqution 6x = 5y + 0 Wht is its slope? Misellneous problems 45 Find the distne between the two points (, ) nd ( 5, 0) 46 Consider the numbers following is true? 057 nd Whih of the () < 057 (b) 057 < () = 057 (d) It is impossible to tell without lultor whih of these numbers is lrger (e) None of the bove 47 Wht is the rnge of the funtion f (x) = 0 (x + 7) + 6? 48 If z = (4x + 5y) then z = 49 Find the domin of the funtion f (x) = Answers x+5 x Vlues of trig funtions t referene ngles Find os ( Find s ( 5 Find sin ( π) 4 Find tn ( 5 Find se ( 7 6 Find ot ( 4 π) Trig identities 7 Give the formul for os (x y) in terms of os x, os x os y + sin x sin y (Trig identities) 8 Give the formul for os (x) in terms of os x nd sin x os x sin x (Trig identities) 9 Give the formul for os (x + y) in terms of os x, os x os y sin x sin y(trig identities) 0 Give the formul for sin (x y) in terms of os x, sin x os y os x sin y (Trig identities) Give the formul for sin (x + y) in terms of os x, sin x os y + os x sin y(trig identities) Give the formul for sin (x) in terms of os x, sin x os x sin y (Trig identities)

3 Lw of osines nd sines In the piture, θ = 4 π, α = π nd = Find α b θ β 4 In the piture, = 5, b =, nd θ = 6π Find b θ (4 5 ) Inverses 5 Let f (x) = x 7 x+5 Find f (x) To find the inverse, we swith x nd y in y = x 7 x+5 nd then solve for y Thus we must solve for y in the eqution, x = y 7 y+5 To solve this we multiply both sides by y + 5 nd this gives y 7 = xy + 5x Now we ollet the terms hving y on one side nd the other terms on the other side After ftoring out y, this yields y ( x) = 5x + 7 Therefore, y = f (x) = 5x+7 x 6 Suppose rx + sx + t = 0 where r 0 Then x = This is just the qudrti formul is s± s 4rt r 7 Find ll solutions to x 4 x + 0 = 0 The nswer x = ± 6 nd x = ± 5 (Solving qudrti equtions nd ftoring) 8 Find ll solutions to x + 5x + 6 = 0 x = nd x = 9 Suppose x + y = 4 nd x 4y = 4 Find x y We multiply the seond eqution by nd then subtrt from the first eqution This yields 7y =, Solution is : { } y = 7 Now we know wht y is, we plug in to the seond eqution to find x Thus x 48 7 = 4, Solution is : { } x = 0 7 Finlly we find x y = For wht vlue of k does the system of equtions, x + y =, x + ky = hve no solution? 6 Word problems A wter tnk is initilly 4 full After dding 4 gllons of wter, it is 7 8 full Wht is the pity of the tnk in gllons? Initilly there re 4x gllons in the tnk where x is the pity of the tnk When we dd 4 this gives us 4 x + 4 whih is given to equl 7 8x gllons Thus we need to solve the eqution, 4 x + 4 = 7 8x for x Solution is : { } x = 5 The perimeter of retngle is 9 times its width If the length of the retngle is 49, find its width Let the width of the retngle be x nd let its length be y Then x+y = 9x Also, we know tht y = 49 Substituting this in, we find x + 98 = 9x, Solution is : {x = 4} Solving inequlities Solve x (x + 5) (x 4) < 0 for x (, 5) (0, 4) (bsolute vlues nd solving inequlities) 4 Solve 5x 5 < 0 for x (, 9) (bsolute vlues nd solving inequlities) 5 Find the solution to the inequlity, 4x < 6

4 The inequlity holds if nd only if 6 < 4x < 6 Therefore, we need to hve 4 < 4x < 8 Sine 4 > 0 we n divide by it nd get < x < Solving Equtions 6 Let y = 7x+5 x 7 Solve for x To solve this we multiply both sides by x 7 nd this gives 7x + 5 = xy 7y Now we ollet the terms hving n x on one side nd the other terms on the other side After ftoring out x, this yields x (7 y) = 7y 5 Therefore, x = 7y 5 7 y 7 Solve for x in the eqution 0 ( + 7x) / + 85x ( + 7x) / = 0 We multiply both sides by ( + 7x) / nd this gives 0 ( + 7x) + 85x = 0 Now we just solve this for x x = 5 8 Find ll positive solutions to (x + 6) = 6 We squre both sides nd get x = 0 nd so x = 0 Simplifying expressions 9 Simplify ( 4 ) 4 0 Simplify xy xy This involves using the rules of exponents The nswer is 8y Simplifying Simplify x +4 + x We hve to dd these Thus we need to put the two frtions over the sme ommon denomintor x (x +4)x + +4) (x x(x +4) = x +x+8 (x +4)x Simplify x 4 + x 6 x+7 (x )(x+) Simplify (exponents nd rdils nd bsolute vlues) 4 Simplify (exponents nd rdils nd bsolute vlues) Simplify differene quotient 5 Suppose f (x) = x + 6x Simplify f(x+h) f(x) h f (x + h) f (x) = (x + h) + 6 (x + h) [ x + 6x ] whih upon multiplying nd nelling is xh + h + 6h It follows tht if we divide by h we get x+6+h Ftoring of polynomils 6 Ftor the polynomil x + x + 4 (x + 7) (x + 6) 7 Ftor the polynomil 6x + 4x + 4 (6x + 7) (x + 6) Composition Of Funtions 8 Suppose f ( ) =, f () =, nd f () = while g () =, g ( ) =, nd g () = Find f (g ( + )) 9 Let f (x) = x + x nd let g (x) = x Find f (g ()) We see g () = nd so f (g ()) = f ( ) = Lines 40 A line hving the eqution y = mx+b psses through the points ( 4, 7) nd (9, ) Find m + b The slope of the line is 8 nd so the eqution of the line is y + 7 = ( 8 ) (x + 4) We need to find the y interept This is obtined when x = 0 Thus y + 7 = ( ) { 8 (4), Solution is : b = 59 } Now m + b = 8 59 = 5 4 Find the eqution of the line through the points ( 4, ), (5, 4) y = 9 x + 9 (lines nd distnes)

5 4 Find the eqution of the line perpendiulr to 8x+ 6y = 6 through (0, 6) y = x + 6 (lines nd distnes) 4 Find the eqution of the line prllel to x + y = nd pssing through (0, 8) y = x + 8 (lines nd distnes) 44 A line hs the eqution 6x = 5y + 0 Wht is its slope? We n put it in slope interept form s follows y = 6 5 x Therefore, the slope is 6 5 Misellneous problems 45 Find the distne between the two points (, ) nd ( 5, 0) (7) + ( ) = Consider the numbers following is true? 057 nd Whih of the () < 057 (b) 057 < () = 057 (d) It is impossible to tell without lultor whih of these numbers is lrger (e) None of the bove = + > + = Wht is the rnge of the funtion f (x) = 0 (x + 7) + 6? All rel numbers 6 48 If z = (4x + 5y) then z = 6x + 40xy + 5y 49 Find the domin of the funtion f (x) = (, ) (, 5 ] x+5 x