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PreCalculus Chapter 01 Review Sheet
Evaluate the function at each specified value and simplify (notation matters).
f  x   2x  3
1.)
 a  f  4
b f   x 
 c  f  x  1
g  x   x2  3
2.)
 a  2g 1  4
b g   x 
 c  g  x  2
2 x  3, x  4
f  x  
 x  1, x  4
4.)  a  f 1
h  x   5 x3  x
3.)
 a  h  2
b h  x  c 
 c  h  2 x 
b  f  4
 c  f  6
Find all real values of x such that f(x)=0.
5.) f  x   x2  5x
6.) f  x  
2x  3
5
7.) f  x   2 x2  7 x  3
Find the domain and range of the function (use interval notation).
8.)
9.)
10.)
Algebraically determine whether the function is even, odd, or neither.
11.) f  x   x 2  5
12.) f  x   3x 4  5x  1
13.) h  x   6 x3  2 x
Use a graphing utility any relative minimum(s) or relative maximum(s). (Calculator)
14.) f  x   x2  8x  7
15.) f  x    x  3
16.) f  x  
2
Use the given functions and graph to evaluate #17. f  x   x2  3x, g  x   x  4
h  x
17.)
a
b
c
d 
e
f
h
f
h  0 
g  3
g g h h  1
f  g  x 
g
f  x 
ln  x 
x
f  x  h  f  x
, h0
h
Find the difference quotient and simplify the result.
18.) f  x   x2  4 x
19.) f  x   7 x
Find the inverse f 1  x  of the function of f.
x7
6
21.) f  x  
2
x 1
Find the value(s) of x for which f(x)=g(x). (Calculator)
20.) f  x  
22.) f  x    x3  4x  3, g  x    x  1
23.) f  x   x2  3, g  x   1
Determine all interval(s) where f(x)>0. (Calculator)
25.) f  x    x3  5x  3
24.) f  x   3 x  2
Draw an example of a function with the following characteristics:
26.)
f  x  is one-to-one AND
f  x   0 on  3,  
27.)
f  x  is not one  to  one AND
f  2   0
Write an equation for the given function (only rigid transformations took place).
28.)
29.)
30.)
Find the domain of the function.
31.) f  x   x3  5x  1
32.) h  x  
3 x
x2
33.) g  x  
6
x x
2