Math 10 Final Eam Study Guide The Final Eam is comprehensive ut identifying the topics covered y it should e simple. Use the previous eams as your primary reviewing tool! This document is to help provide you with more specific eamples related to functions and function notation. These concepts are thoroughly covered y the tetoo ut are not isolated to any particular section or chapter. Every chapter (ecept chapter ) contains prolems related to evaluating functions at particular values and solving equations/inequalities involving function notation. 1. Know the difference etween an equation, an epression and a function. Know which instruction might e associated with each, i.e., simplify, solve and graph.. Be ale to graph any of the following ase functions with left/right and/or up/down shifts. a. Linear. Asolute value c. Cuic d. Radical e. Rational f. Quadratic g. Eponential h. Log. Be ale to recognize the difference etween rational, irrational, and imaginary numers. Refer to Eam 4. 4. Functions and their inverses. The 4 Biggies. Handout with solutions is availale on the wesite.
Use the following functions to respond to questions 5 through 1. Rationalize all denominators. Use i notation with imaginary solutions. f( 5 g ( ( ) 1 p ( 1 ( log h( r ( 5 1 q( w ( ) 6 n ( ) ( ) j ( ) log ( 1) 5. Use interval notation to identify the domain and range of any of the functions listed aove (ecept n( and j(. 6. Evaluate and simplify. f () 7. Find all values of for which a) f ( p( ) r ( c) g ( ) 1 d) w( p( e) w ( 0 f) h ( ) n ( ) g) ( h) ( ) j ( ) 8. Find 1 ( 9. Find p( f( )) 10. Rewrite w( in verte form. w( 11. Use long division or synthetic division to perform. p( 1. Evaluate and simplify. w ( ) w()
Math 10 Selected Solutions to the Final Eam Study Guide 1. Know the difference etween an equation, an epression and a function. Know which instruction might e associated with each, i.e., simplify, solve and graph.. Be ale to graph any of the following ase functions with left/right and/or up/down shifts. i. Linear e) Rational j. Asolute value f) Quadratic. Cuic g) Eponential l. Radical h) Logarithm. Be ale to recognize the difference etween rational, irrational, and imaginary numers. Refer to Eam 4. Eamples of: Rational numers: Irrational numers: 7 1 6,, 5,0, 11, 8, e,, 5, 5 Imaginary numers:, i 4, 18 4. Functions and their inverses. The 4 Biggies. Handout with solutions is availale on the wesite.
Use the following functions to respond to questions 5 through 1. Rationalize all denominators. Use i notation with imaginary solutions. f( 5 g ( ( ) 1 p ( 1 ( log h( r ( 5 1 q( w ( ) 6 n ( ) ( ) j ( ) log ( 1) 5. Use interval notation to identify the domain and range of any of the function listed aove. g ( ( ) 1 Domain: All reals., Range: Since the verte is at, 1 and the paraola opens up, the 1, range is all y-values greater than or equal to -1. f( 5 Domain: The value in the square root must not e negative. 5 0 5 5, h ( Domain: All reals., Range: The y values are all positives. 0, ( log This is the inverse of h(. Domain and range are switched. Domain: 0, Range:, 6. Evaluate f () 5 7 7 7 7 7 7
7. Find all values of for which a) f ( p( 5 1 Square oth sides 5 1 Now it is quadratic. 0 4 Zero product property. Chec your solutions. ) r ( 5 Cue oth sides c) g ( ) 1 ( ) 1 1 Add one to oth sides. ( ) 0 Square root rule. (two solutions) d) w( p( 6 1 set = 0 5 0 Doesn t factor. Use another method. e) w ( 0 6 0 Doesn t factor. Try completing the square. f) h ( ) n ( ) ( Same ases, therefore eponents are equal. Now solve for. g) ( log Translate into an eponent equation. 9 h) ( ) j ( ) log log ( 1) Same ases. Arguments are equal. 1 Now solve for.
8. Find 1 ( To find the inverse, switch and y and then solve for y =. You will need to translate from logarithm to eponent to succeed. p f p( f( )) p 5 9. Find ( ( )) p 1 or 1. 10. Rewrite w( in verte form. Change to the form of the function that indicates where the verte is. Solution: w ( ) 1 5 w( 11. Use long division or synthetic division to perform. p( Note: p( is 1 1 Then w p ( ) 1 ( ) 6 Long division: 1 6 Synthetic division: 1 1 6 1. Evaluate and simplify. w ( ) w() w ( ) w() 6 6 = 4 4 46 14 614 14 6 6