Name _____________________ Page 1 of 14 Algebra 2 – Second Semester Exam Review 1) Simplify. Write using positive exponents only. a) 3 2 ( 16) (Section 6.1 and 6.2) b) 4 3 ( 64) (Section 6.1 and 6.2) c) 8 5 4 16 xy (Section 6.2) d) 3 3 36 96 (Section 6.2) 2) For the functions 2 () 3 5 2 fx x x and 2 () 2 8 gx x , (a) evaluate () () fx gx and (b) evaluate () () fx gx . (Section 6.3) 3) For the functions 3 () 18 fx x and 4 3 () gx x , evaluate ( ( )) fgx (Section 6.4) 4) Given the relation below: (a) write the inverse relation and (b) determine ) 0 ( 1 f ? (Section 6.4) 5) Determine the inverse of the function: (Section 6.4) x 0 1 2 3 ) ( x f 8 4 0 -4
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Name _____________________
Page 1 of 14
Algebra 2 – Second Semester Exam Review
1) Simplify. Write using positive exponents only.
a) 32( 16) (Section 6.1 and 6.2)
b) 43( 64) (Section 6.1 and 6.2)
c) 8 54 16x y (Section 6.2)
d) 3 33 6 9 6 (Section 6.2)
2) For the functions 2( ) 3 5 2f x x x and 2( ) 2 8g x x , (a) evaluate ( ) ( )f x g x and
(b) evaluate ( ) ( )f x g x . (Section 6.3)
3) For the functions 3( ) 18f x x and
4
3( )g x x , evaluate ( ( ))f g x (Section 6.4)
4) Given the relation below: (a) write the inverse relation and (b) determine )0(1f ? (Section 6.4)
5) Determine the inverse of the function: (Section 6.4)
x 0 1 2 3
)(xf 8 4 0 -4
Page 2 of 14
6) Graph 2)( 2 xxf for 0x and )(1 xf on the same graph.
(Section 6.4)
7) Evaluate: 4
1log
64
(Section 7.4)
8) Evaluate: 3log 243 (Section 7.4)
9) Write the equation log10,000 4 in exponent form. (Section 7.4)
10) Write the equation 4log 64 3 in exponent form. (Section 7.4)
11) Write the equation ln 1e in exponent form. (Section 7.4)
12) Expand: 2
3
4ln
x
y
(Section 7.5)
13) Condense: log9 2log 3log3y x (Section 7.5)
14) Solve: ln(2 1) 5x (round to the nearest hundredth) (Section 7.6)
15) Solve for x: 23log ( 2) 6x (Section 7.6)
Page 3 of 14
16) Solve for x: log 243 5x (Section 7.6)
17) Solve for x: 34log 3 28x (Section 7.6)
18) Determine the value of x: 10 4 10x (round to 3 decimal places) (Section 7.6)
19) Solve: 42 14
3 3
xe (round to 3 decimal places) (Section 7.6)
20) Solve: 2 15 30x (round to 3 decimal places) (Section 7.5 and 7.6)
21) For each of the graphs below, name the type of function shown in the graph and answer the question:
“Does that family of functions have asymptotic behavior?” If yes, give the equation of the asymptote(s).
(Sections 4.2, 6.5, 7.1, 8.2)
a) b)
c) d)
Page 4 of 14
22) Graph. Include the equation of the asymptote when necessary. Name the type of function shown in your