Algebra practice worksheets

Algebra practice Name Directions: Show all work on a separate piece of paper. Place your final answer on this sheet. 1. Given g ( x)  3 x 1 a. Evaluate and simplify completely i) g (2) = ii) g (0) = iii) g (1) = iv) g (4) = v) g ( x  3) = b. Solve algebraically for exact x iii) g ( x)  2  4 x= f x  h   f x  2. Simply the difference quotient for the following functions [different quotient ] h f x  h   f x  a) f x   x 2  2 x  3 = h b) f x   x3  5 c) f x   i) g ( x)  5 x= ii) g ( x  2)  4 x= f x  h   f x  = h f x  h   f x  = h 4 x 3. Simplify the following completely with a common denominator. Your final answer will not contain any negative exponents. b  2x = 4 x 5x  2  a) = b) x 1 2x b  24 x2 1 x2 1  x 2 x  1  2t 2 x c) d) =  2 t 3= 2 t 3 x2 1    1  2 3  e) = x5 x5 g) 4z  2 2  2 z z  2 f) z2 h) e x e1 x = 1 2 = a n 3n 1 = 3n a n 1 i) x 3  1  6 x3 x3  1 3  x 2 1   4 = j) 5 1 z 2  3 1  z2 = k) 2x  x  5 2   1 2  x x 5 x2  5 2 2   1 2  2x = l) x  h  1 2  1 x2 h = m) 1  x 1  x2 1 y = 1 y2 n) 3 3 1 x 1 = 4. Solve algebraically for the exact solution(s). Solve for the indicated variable. Assume all other variables are constants. 1  ax  4b x  __________ e5 x  e5 x  1 x  __________ x2 x  __________ y  _________ p  _________ log( x)  log( x  21)  2 x  __________ a b  1 x 2x 6 y 2  y  0 t  __________ 10te3t  2t 2e3t  0  p  1 p 2  11  0  p  2 p  3 t  __________ 3t  12(.8)t x  __________ x  __________ ln(t  2)  ln(t )  ln 7 y  _________ x  1  10  2 3 x 2 y  x3  22 y  3 x  __________ 3  x   13 x  __________ 9 xe ax  3x2eax  0 x  __________ ln(ln( x))  1 x  __________ A(.83) x  B(b) x x  __________ x  4x  2  7 x  __________ 4 xe x  3e x  0 y  _________ x  __________ 3(ax  1)  2 x  4(a  ax) x  __________ x  1x  3  15 x  __________ x  __________ log( x)  log( x  1)  1 3x 2 1   5 x 5 x  __________ logx  4  2  logx  1 x  __________ 4x  1  5  0 2 5y  2 0 y2 1 4y 20 1 2y z  __________ 0  4 z 3  6 z 2  24 z  36 t  __________ t 2  t  6  14 y  _________ t  __________ 2t  (3t  4)  5(t  2) y  _________ x2  2y  y3 x y  __________ Ax  By  C  0 t  __________ ln(t  2)  ln(t )  ln( ) t  __________ t 3  16t 1  0 3 p2  p  2 0 p  _________ p7 R  _________ 1 1 1   R a b 5. Determine if each statement is Correct or Incorrect. Circle the correct answer. C I x 2  121  x  11 w 1 2  1 for w  1 w 1 2 ln( M ) ln( B) C I 4  2 C I x3 3  x3 3 9 C I C I ln e xe y  x  y   C I eln(x )  5  xe5 C I 2x  y  2x  2 y C I ln( M )  ln( B)  C I ln a    1 ln a  2 C I log abt  t logab C I   C I ln e x  e y  x  y C I   C I 3 r 3  64  r  4 2 x 1  2 2  2 x x 3 3 x 2  3x  1  3x  1 x2 C I e3  e9 C I 82t  1  4t  2 C I e  x 2  e2 x C I 1 1  x4 4 x C I x  12  2x  1  x  1x  3 1 3 C I 1 4  3t  4 3t 1 ab  1 a b ab 1 C I ln(1)  e C I  z  8 2   z  8 2 3 C I C I 2t  t ln(2) C I 1 1 1   x2 x 2 log( x) ln( x) C I  log( t ) ln(t ) C I e4 ln(x )  4 x C I Ax 2  B  Ax  B x C I log( x  y)  log( x) log( y) C I If f ( x)  5x , then f x  4  5x  4 C I 1  y 3  1  y3