final (math) review - Overview For each function f(x find...

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Overview For each function, f ( x ), find the (a) domain, (b) range, (c) asymptotes, (d) x-intercepts, (e) y-intercepts, and finally (f) sketch f ( x ). 1 . f ( x ) = x 2 . f ( x ) = x 2 3 . f ( x ) = x 3 4 . f ( x ) = | x | 5 . f ( x ) = x 6 . f ( x ) = 1 x 7 . f ( x ) = ln x 8 . f ( x ) = e x 9 . f ( x ) = sin x 10 . f ( x ) = cos x 11 . f ( x ) = tan x Chapters 1 and 2 Graph f(x) and determine domain and range: 1 . f ( x ) = | x | , - 2 < x < 1 2 , 1 x 2 7 - 2 x, 2 < x 3 Solve for f - 1 ( x ) if it exists and if it doesn’t, explain why. 2 . f ( x ) = 3 x 3 + 1 3 . f ( x ) = 1 - x 2 , x 0 Complete the square to find the vertex and then graph f ( x ): 4 . f ( x ) = - 3 x 2 + 6 x + 2 For a small h = 0, (a) draw a secant line through the points (1,f(1)) and (1+h,f(1+h)), and (b) determine the average rate of change of f ( x ) between x = 1, and x = 1 + h . 5 . f ( x ) = 1 - x 6 . f ( x ) = x 3 + x Solve the given inequality for x and express the solution as a line graph and in interval notation 7 . x - 1 x +2 < 0 8 . - 2 x 2 + 5 x + 3 0 9 . 6 - 3 | 2 x + 1 | ≤ 0 10 . 5 - | 4 x - 3 | > 0 Chapters 3 and 4 For the given polynomial, p ( x ), (a) find the real quadratic and linear factorization, (b) list all zeros with their multiplicities (e.g. 1 mult. 2, ...)
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