Practice Page
Directions: Read carefully. Choose the best answers.

1.
Given: functions f (x) and g(x) as shown at the right.
Which function has the greater average rate of change on the interval [-1,1] ?
f (x) = 3x3 - 2x2 + 4

x
g(x)
-2
1.25
-1
2.5
0
5
1
10
2
20
 
Choose:
 
function f (x) is greater by 0.75
 
function g (x) is greater by 0.75
 
function f (x) is greater by 0.5
 
function g (x) is greater by 0.5

 

 

2.
Given: functions f (x) and g(x) as shown at the right.
Which function has the larger x-intercept?
f (x) = ln(x + 1)

x
g(x)
-1
4
0
2
1
0
2
-2
3
-4
 
Choose:
 
function f (x) with x-intercept (0,0)
 
function g (x) with x-intercept (1,0)
 
function f (x) with x-intercept (2,0)
 
function g (x) with x-intecept (2,0)

 

 

3.
Given: the graph shown at the right and
g (x) = 2 | x | - 1.
In how many places will these two graphs intersect?
comparegraph2  

Choose:
 
one
 
two
 
three
 
four

 

 

4.
Given: f (x) = ex and g(x) = x + 2
Find the value(s) of x (to the nearest hundredth) where
f (x) = g(x).
    

Choose:
 
-1.92 and 1.30
 
-1.84 and 1.15
 
0.16 and 3.15
 
0.16 and 3.14

 

 

5.
Three boats are traveling according to the following representations. Look at each of the representations to determine the speed of each boat.
Boat A: y = 30x
where x = time (hours) and
y = distance (miles)

Boat B
Time (hrs)
Distance (miles)
2
70
4
140
6
210
10
350
boata

List the boats, in order, from fastest to slowest:
Choose:
 
Boat A, Boat B, Boat C
 
Boat C, Boat B, Boat A
 
Boat B, Boat A, Boat C
 
Boat B, Boat C, Boat A

 

 

6.
Which of the following functions has a minimum value that is less than the one shown in the graph at the right?

Choose:
 
m (x) = x2 - 2x - 10
 
g (x) = x2 - 6x + 7
 
h (x) = | x + 3 | - 6
 
r (x) = | x - 8 | + 2
lessgraph2

 

 

7.
new2
Which of these characteristics are shared by all three functions?
(Check all that apply, and hit SUBMIT!)

domain (-∞,∞)

range (-∞,∞)

passes through the point (2,4)

passes through the origin

has points lying in quadrant II

positive values on interval (0,∞)

one relative minimum point

as x → ∞, y → ∞

as x → -∞, y → ∞

increasing on interval (0,∞)

increasing on interval (-∞, 0)

     

 

 

 

8.
Given functions p(x) and m(x) as shown below:

p(x) = -x2 - x + 6

x
-3
-2
-1
0
1
2
3
4
5
m(x)
-7
0
5
8
9
8
5
0
-7

Which of the following statements regarding these functions is TRUE?
   

Choose:
 
The function p(x) has a greater maximum value than m(x).
 
The sum of the roots of m(x) = 0 is greater than the sum of the roots of p(x) = 0.
 
The y-intercept of p(x) is greater than the y-intercept of m(x).
 
Over the interval [-1,1], the average rate of change for m(x) is less than that for p(x).

 

 

9.
Which of the following statements is TRUE regarding functions f (x) and
g(x) shown at the right?

Choose:
 
g(x) has a greater rate of change than f (x).
 
f (x) has a greater rate of change than g(x).
  Both functions have the same rate of change.
  There is insufficient information to determine the rate of change.
x
f (x)
-1
5
0
3
1
1
2
-1

gx2

 

 

10.
Which of the following functions has the greatest rate of change over the interval [-1, 1]?

Choose:
 
c101
  

x
-2
-1
0
1
g(x)
-1
-½
0
½
 
c102

x
-2
-1
0
1
m(x)
5
3
1
-1

 

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