Summer Review Packet for Students Entering Pre-Calculus By: 2x3 + 3x2 - 6.x + 10 Summer Review Packet for Students Entering Pre-Calculus x+3 67 . f ( xx ) = x2 - 6x+2 68. g(x) = 6x-7 69 . f ( x ) = 3x 3 - 4 Long Division Synthetic Division f (3) =_ g ( x + h) =_ 5 [f ( x + 2) ] = 2x3 + 3x2 - 6x+10 2x3 + 3x2 - 6x + 10 x+3 x+3 espia rhod aduo 2 x 2 - 3 x + 3 + 1 x + 3 * + 3 ) 2x3 + 3x2 - 6x +10 2x3 + 3x2 - 6x + 10 x+3 (-)(2x3+6x2) grolevion -3 2 3 -6 10 -3x2 - 6.x -6 9 (-)(-3x2-9x) 2 - 3 3x + 10 = 2x- 3x+3+1 x + 3 (-) (3x+9) Composition and Inverses of Functions: Recall: (f g)(x) = f(g(x)) ORf[g(x)] read "f of g of x" means to plug the inside function in for x in the outside function . Divide each polynomial using long division OR synthetic division. Example : Given f ( x ) = 2x3 +1 and g(x) = x-4 find f(8(x)). 65. C - 302 + 18c-16 66, x4 -2x2 - x+2 f(8(x) ) = f(x-4) c' +30-2 x+2 =2(x-4)2+1 = 2(x2 - 8x+16)+1 = 2x2 -16x+32+1 f(8 (x) ) = 2x2 -16x+33 Suppose f(x) = 2x, g(x) =3x-2, and h(x) = x2 -4. Find the following: 70. f [8 (2) ] = 71. f[8(x) ] = 72 . f [ h ( 3 ) ] = 73. 8[ f ( x ) ] = To evaluate a function for the given value, simply plug the value into the function for x. Evaluate each function for the given value . To find the inverse of a function, simply switch the x and the y and solve for the new "y" value. 14