Pre-Calculus: Chapter 1Review
Name___________________
1. Given A = {-2, 0, 2, 4} and B = {5,6,7}, Which set of ordered pairs is NOT a
function?
a. (-2,5), (0,7), (2,6)
b. (0,6), (-2,6), (2,6), (4,6)
c. (4,5), (2,6), (0,5), (-2,7)
d. (0,5), (2,6), (4,7), (2,6)
2.
 x 2  1, x  2
Given f ( x)  
 , Graph the piecewise function by hand and then
2x - 3, x  2 
find f (5) .
f ( x  4)  f (4)
,x  0
x
3.
If f ( x)  x 2  4 x , find
4.
Find the domain and range of the function f ( x) 
interval notation in you answer.
1
. Make sure you use
x  5x  6
2
5.
Find the domain and range of f ( x)  16  x 2 .
6.
Graph for the following piecewise function:
3x  4, x  2
f ( x)   2

x , x  2 
7.
For the function f ( x)  ( x  2)(x  2)(x  5) , determine any relative maximum or
minimum, then determine the open intervals in which the function is increasing,
decreasing, or constant. If necessary, round to three decimal places.
8.
For the function f ( x)  x 3  5 x 2 , determine any relative maximum or minimum,
then determine the open intervals in which the function is increasing, decreasing,
or constant. If necessary, round to three decimal places.
9.
Is the following function even, odd, or neither? f ( x)  3x 3  2 x 2
10.
Use the graphing utility to determine the interval(s) on the real axis for which
f ( x)  0 for f ( x)  16  x 2
11.
Describe the transformation of the graph of f ( x)  x 2 for the graph of
g ( x)  ( x  9) 2  4
12.
Which graph below represents g ( x)  x  2  3
a.
b.
c.
d.
13.
Which graph represents g ( x)  x 2  3
a.
b.
c.
d.
14.
Given f ( x)  4 x  1 and g ( x)  6  x find ( f  g )(5) .
15.
Find the functions f and g such that ( f  g )(x)  h( x) : h( x) 
16.
Given f ( x) 
1
x 6
5
1
and g ( x)  x  3 , find the domain and range of ( f  g )(x) .
x 3
Make sure you simplify the denominator.
2
17.
18.
In which graph(s) do y represent a one-to-one function(s) of x?
a.
b.
c.
d.
Determine which function is one-to-one.
a.
y  x 3
b. y  7  x
c. y  x 2  3
d. y  x 2  4
e. None of these
19.
Given f ( x)  6  x , find its inverse.
20.
Given f ( x)  2 x 2 and g ( x)  3x  1 , find ( f  g )( x) . Please simplify the
expression.
1
 g 1 )( 2) .
21.
Given f ( x)  2 x 2 and g ( x)  3x  1 , find ( f
22.
Find the value(s) of the x for which f ( x)  g ( x)
f ( x )  x 2  3 g ( x)  x  3
23.
The table below gives the average growth in inches of a wooded tract of land in
terms of the monthly rainfall in inches. Use the regression capabilities of a
graphing utility to find a linear model that gives the growth g, in terms of the
monthly rainfall r. Then use the linear model and a graphing utility to determine
the amount of growth if it rains 1.2 inches. Please round your answers to three
decimal places.
Monthly
Rainfall, r,
in inches
Growth, g,
in inches
0.10
0.20
0.70
1.20
0.40
0.75
2.6
2.5
3.0
3.4
2.75
3.1