Math 203 - Intermediate Algebra
Professor Valdez
Chapters 8 & 9 Review for Final
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question.
Solve the formula for the indicated letter.
1) A = 1 πr2 for r > 0
3
1)
Solve.
2) (9x + 3)2 - 6 = 0
2)
3) x2 - 2 x = - 7
3
6
3)
Solve the problem.
4) The weekly revenue R of a company that sells x toy trucks is
given by R = x(35 - 0.004x).
4)
How many units must be sold so the company makes a weekly
revenue of $60,000?
Use the discriminant to determine the number and type of solutions for the equation.
5) x2 - 7x - 1 = 0
5)
Use the discriminant of the equation to determine the number of x-intercepts.
6) f(x) = 4x2 - 8x + 4
6)
7) f(x) = x2 + 8x + 21
7)
Graph the function function.
8) f(x) = -x2 + 2x + 3
8)
Solve the problem.
9) The cost in millions of dollars for a company to manufacture x
thousand automobiles is given by the function
C(x) = 3x2 - 24x + 128. Find the number of automobiles that
must be produced to minimize the cost.
1
9)
10) A toy rocket is launched straight upward with an initial velocity
of 32 feet per second from a 4-foot high platform. The height h,
in feet, of the rocket above ground t sec after it is launched is
modeled by the function h(t) = -16t 2 + 32t + 4.
10)
i) When will the rocket reach its maximum height? What is that
height?
ii) How many seconds does it take until the rocket hits the
ground? Round to the nearest tenth of a second if necessary.
Solve the equation.
11) x4 - 4x2 + 3 = 0
11)
12) (m + 4)2/3 + 9(m + 4)1/3 + 20 = 0
12)
Write a quadratic equation having the given numbers as solutions.
13) 9, only solution
13)
14) - 4 , 7
5
14)
15) 2i, -2i
15)
Solve. Then graph the solution.
16) x2 - 2x - 15 < 0
16)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
17) 4x + 7 ≤ 0
x-2
17)
Graph the function function.
18) f(x) = 5(3)x
18)
Given f(x) and g(x), perform the indicated operation.
19) f(x) = 4 ; g(x) = -4
x+4
x-4
Find (f + g)(x).
2
19)
20) f(x) = x + 4 ; g(x) =
Find (f · g)(x).
x -4
20)
Given f(x) and g(x), find the composition.
21) f(x) = 4x2 + 4x + 8; g(x) = 4x - 6
Find (g ∘ f)(x).
21)
3
22) f(x) =
x; g(x) = 2x - 1
Find (f ∘ g)(-13).
22)
Evaluate.
23) Find (f/g)(4) given f(x) = -8x + 2 and g(x) = 2x2 + 2.
23)
Determine whether the function whose graph is shown is a one-to-one function.
24)
24)
y
x
Given the graph of a one-to-one function, sketch the graph of its inverse.
25)
25)
y
10
5
-10
-5
5
10
x
-5
-10
Find the inverse of the function represented by the set of ordered pairs.
26) f: {(-1, 14), (11, -14), (-20, 10)}
26)
3
Find the inverse of the following one-to-one function.
27) f(x) = 7x - 4
28) f(x) =
5
x+2
28)
Decide whether or not the functions are inverses of each other.
29) f(x) = 9 + 4 , g(x) = -4
x
x-9
30) f(x) =
3
27)
3
7x - 8 , g(x) = x + 8
7
29)
30)
Evaluate the function for the given value.
31) f(x) = 6 1-x; f(4)
31)
Solve.
32) 2 7 + 3x = 1
4
32)
Solve the problem.
33) The number of bacteria growing in an incubation culture
increases with time according to B(x) = 9500(3)x, where x is time
in days. What was the initial number of bacteria in the incubation
culture?
34) The half-life of a certain radioactive substance is 14 years.
Suppose that at time t = 0 , there are 27 g of the substance.
Then after t years, the number of grams of the substance
t/28
remaining will be N(t) = 27 1
. How many grams of the
2
33)
34)
substance will remain after 70 years? Round to the nearest
tenth.
35) What will be the amount in an account with initial principal
$5000 if interest is compounded continuously at an annual rate
of 3.25% for 6 years?
Write the logarithmic equation in its equivalent exponential form.
36) log 7 49 = 2
4
35)
36)
Write the exponential equation in its equivalent logarithmic form.
-2
37) 1
= 25
5
Solve. Round the answer to three decimal places.
38) 4 x-3 = 21
37)
38)
Evaluate.
39) log 8 1
64
39)
40) log 5
40)
5
41) log 2 1
41)
Write the expression as the sum or difference of logarithms.
42) log (16·9)
4
43) log m m + 16
m + 13
Evaluate.
44) log
5
42)
43)
5 19
44)
45) ln e 9x
45)
46) 10 log 9
46)
47) The formula for the pH of a solution is given by the logarithmic
equation pH = -log [H+ ], where [H+ ] is the concentration of
hydrogen ions. The concentration of hydrogen ions of a specific
solution is 10 -6 . Calculate the pH of this solution.
47)
Solve.
Provide an appropriate response.
48) Write the expression as a single logarithm:
5 log b (x - 3) - 6 log b x
5
48)
Write the expression as the sum or difference of logarithms.
4
x9 b 8
49) log b
y2
49)
Solve.
50) log 4 x = 3
50)
51) log 8 2 = x
51)
52) log 2 (x + 4) + log 2 (x - 2) = 4
52)
Use a calculator to approximate the logarithm to four decimal places.
53) log 100 20
53)
Solve the problem.
54) The size P of a rabbit population at time t (in years) is modeled
by the function P(t) = 600e0.16t .
54)
After how many years will the population reach 3000? Round to
the nearest hundredth.
55) $6500 is invested at 4% compounded quarterly. In how many
years will the account have grown to $8000? Round your answer
to the nearest tenth of a year.
6
55)
Answer Key
Testname: CHAPTERS 8 AND 9 REVIEW
1) r
=
3A
π
2)
-3 +
9
6 , -3 - 6
9
3)
2 + i 38 , 2 - i 38
6
6
4) 2340 units
5) Two real-number solutions
6) One x-intercept
7) No x-intercepts
8) Vertex: (1,4); axis of sym: x
= 1; x-intercepts: (-1,0), (3,0); y-intercept: (0,3)
y
10
5
-10
-5
10 x
5
-5
-10
9) 4
10) i)
thousand automobiles
20 ft in 1 sec
ii) 2.1 sec
11) ±1, ± 3
12) -129, -68
13) x2 - 18x + 81 = 0
14) 5x2 - 31x - 28 = 0
15) x2 + 4 = 0
16) (-3, 5)
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
17)
- 7, 2
4
-6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
7
Answer Key
Testname: CHAPTERS 8 AND 9 REVIEW
18)
y
8
6
4
2
-8
-6
-4
-2
2
4
8 x
6
-2
-4
-6
-8
19)
-32 , x ≠ -4, 4
x2 - 16
20) x
- 16
21) (g ∘ f)(x) = 16x2 + 16x + 26
22) -3
15
23) 17
24) Not
25)
one-to-one
y
10
5
-10
-5
5
10
x
-5
-10
26) f-1 :
{(14, -1), (-14, 11), (10, -20)}
27) f-1 (x) = x + 4
7
28) f-1 (x)
= -2x + 5
x
29) Not inverses
30) Inverses
8
Answer Key
Testname: CHAPTERS 8 AND 9 REVIEW
31)
1
216
32) -3
33) 9500
34) 4.8 g
35) $6076.55
36) 7 2 = 49
37) log 1/5 25
= -2
38) 5.196
39) -2
40)
1
2
41) 0
42) 2
9
4
43) log
m (m + 16 ) - log m (m + 13 )
44) 19
45) 9x
46) 9
47) 6
(x - 3)5
48) log
b
x6
49)
+ log
9 log x + 2 - 2log y
b
b
4
50) 64
51)
1
3
52) 4
53) 0.6505
54) 10.06 yr
55) 5.2 years
9