(2.5) 1. Solve the following compound inequality and graph the solution set.

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1 Intermediate Algebra Practice Final Math 0 (7 th ed.) (Ch. -) (.5). Solve the following compound inequalit and graph the solution set. 0 and and > or or (.7). Solve the following absolute value inequalities. Write our answer in interval notation > 9 + < + (.5). Find the equation of the line satisfing the given conditions. Write our answer in the form: = m + b slope ; through (, ) through (, ) and (, ) undefined slope; through (, ) zero slope; through (, ) (.,.). Find the intercepts of the following equations. = = -intercept: -intercept: -intercept: -intercept: Revised -9- LC No part of this work ma be reproduced without the prior written consent of the Cerritos College Math Learning Center.

2 Math 0 Practice Final (cont.) (.) 5. Find the domain and range of the following relations.* domain: range: domain: range: *You should practice more problems like these! Look in our e-tet/tetbook. See eample on pages -7 and work problems 9-0 on page. (.). Graph the piecewise function: f ( ) = if < 0 + if 0 g( ) if = + if < 0 0 (.) 7. Solve the following sstem of equations. + = = + = 5 + = + = 9 + = 7 = = No part of this work ma be reproduced without the prior written consent of the Cerritos College Math Learning Center.

3 Math 0 Practice Final (cont.) (5., 5.). Simplif. Write our answer using positive eponents onl. 7 5 ( ) a b ab 9 z (5.7) 9. Factor the following polnomials completel (.,.). Perform the indicated operations. Simplif if possible (.). Simplif the following comple fractions (7.). Simplif. Assume all variables represent positive real numbers. 7 a b 5r 9 s 5 (7.5). Rationalize the denominator. 5 + No part of this work ma be reproduced without the prior written consent of the Cerritos College Math Learning Center.

4 Math 0 Practice Final (cont.) (5.,.5, 7.,.,.) Solve the following equations.. + = =. + = 7. m 7m=. = 9. + = 5 (.5,.) 0. Graph the following functions. Find the verte and and intercepts if the eist. f ( ) = ( ) + ( ) ( ) f = + verte: verte: -intercept: -intercept: -intercept: -intercept: 0 0 No part of this work ma be reproduced without the prior written consent of the Cerritos College Math Learning Center.

5 Math 0 Practice Final (cont.) f ( ) = ( + 5) f ( ) ( ) = verte: verte: -intercept: -intercept: -intercept: -intercept: 0 0 (.). Solve the following nonlinear inequalities. Write the solution in interval notation. ( 7)( + ) > 0 ( )( ) 7 + < 0 + < 0 + > 0 (9.). For the functions, f ( ) = and g( ) = +, find ( f g)( ) and ( g f )( ). For the functions, f ( ) = and g( ) =, find ( f g)( ) and ( g f )( ). No part of this work ma be reproduced without the prior written consent of the Cerritos College Math Learning Center. 5

6 Math 0 Practice Final (cont.) (9.). Find the inverse of the following one-to-one functions. f ( ) = 5 f ( ) f ( ) = ( + 5) ( ) = 7 f = 7 (9.). Write the following epression as a sum or difference of logarithms. 5 7 ( ) log z 5 log 7 z (9., 9.) Solve the following equations. Give an eact solution = 5 = 5. log + log ( + ) = ( ) log log = (.7) 7. Graph the following inequalities. < No part of this work ma be reproduced without the prior written consent of the Cerritos College Math Learning Center.

7 Math 0 Practice Final (cont.) ANSWERS:. [, 0 ] or { 0} (, ) or { > } [ ] - 0 (, ] [, ) or { or } ] [ - - (, ) or { is a real number}. [, ] (,) (, ) (, ) 5. = + = = =. -intercept: ( 5,0 ) and ( 7,0) -intercept: (, 0 ) -intercept: ( 0, 5) -intercept: 0, 5 5. domain: (, ) domain: (, ] [, ) range: (,5] range: (, ). ( No part of this work ma be reproduced without the prior written consent of the Cerritos College Math Learning Center. 7

8 Math 0 Practice Final (cont.) 7., (, ) ( ) {, = }. 7 b 7a 5 z 9. ( + )( 5+ ) ( )( + 5) ( 5 ). ( + ) ( + ) ( + ) ( + ) ( ) + ( + ) ( + ) ( ). + + or. ab b 5r s. 5 or 7 7 ( ) + or. = 9 (note: = does not check) 5. = (note: = 5 does not check).. ± = 7. = or = 9. 7 ± 5 m = 7 = 5 or = No part of this work ma be reproduced without the prior written consent of the Cerritos College Math Learning Center.

9 Math 0 Practice Final (cont.) 0. verte: (, ) verte: (, ) -intercept: none -intercept: (,0 ) and (,0) -intercept: ( 0, ) -intercept: ( 0, ) verte: ( 5,0) verte: (, ) -intercept: ( 5,0) -intercept: (,0 ) and (,0) -intercept: ( 0, 5) -intercept: ( 0, ). ( ) 7,, (,) 7,,, ( ) ( ) ( f g )( ). ( g f )( ) = 9 = 9 ( f g )( ) ( g f )( ) = = + 5. f ( ) = f ( ) f ( ) = 5 ( ) 7 + = f = + 7 No part of this work ma be reproduced without the prior written consent of the Cerritos College Math Learning Center. 9

10 Math 0 Practice Final (cont.). 5log7 + log7 + log7 z 5log7 log7 log7 z 5. = =. = (note: = does not check) no solution (note: = 9 does not check) 7. Graph the following inequalities. < + 0 No part of this work ma be reproduced without the prior written consent of the Cerritos College Math Learning Center.

Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1

Math 030 Review for Final Exam Revised Fall 2010 RH/ DM 1 Math 00 Review for Final Eam Revised Fall 010 RH/ DM 1 1. Solve the equations: (-1) (7) (-) (-1) () 1 1 1 1 f. 1 g. h. 1 11 i. 9. Solve the following equations for the given variable: 1 Solve for. D ab