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MAT 1073 Test 3 Review Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Evaluate the expression using the values given in the table.
- Given the graphs of functions f and g.
Find (f∘g)(-3).
A) - 3 B) 1 C) 0 D) 2
For the given functions f and g, find the requested composite function value.
- f(x) = 2x + 2, g(x) = 4x^2 + 3; Find (g ∘ f)(2). A) 1447 B) 147 C) 14 D) 40
Find the indicated composition for the given pair of functions.
- (f ∘ g)(x): f(x) = x + 2 , g(x) = 8x - 6
A) 2 2x (^) - 1 B) 8 x (^) + 2 - 6 C) 2 2x (^) + 1 D) 8 x (^) - 4
For the given functions f and g, find the requested composite function.
- f(x) = (^) x 3
, g(x) = (^) 3x^2 ; Find (f ∘ g)(x).
A) 3 x 2 - 6x
B) 9 x 2 + 6x
C) 9 x 2 - 6x
D) 2 x^ -^4 9x
Decide whether the composite functions, f (^) ∘ g and g (^) ∘ f, are equal to x, respectively.
- f(x) (^) = x3^ + 1, g(x) (^) =
x (^) - 1
A) Yes, yes B) Yes, no C) No, yes D) No, no
Indicate whether the function is one-to-one.
- {( 6 , - 12 ), ( 11 , - 11 ), ( 9 , - 10 ), ( 7 , - 9 )}
A) Yes B) No
Find the domain of the composite function f ∘ g.
- f(x) (^) = 2 x + 9
; g(x) (^) = x (^) + 7
A) {x x ≠ - 9 } B) {x x ≠ - 9 , x ≠ - 7 } C) {x x ≠ - 16 } D) {x x is any real number}
- f(x) = (^) x- 6
; g(x) = - x^48
A) {x x is any real number} B) {x x (^) ≠ 0, x (^) ≠ - 8 } C) {x x (^) ≠ 0, x (^) ≠ 6 } D) {x x (^) ≠ 0, x (^) ≠ - 8 , x (^) ≠ 6 }
- f(x) = x - 1 ; g(x) = 1 x - 9
A) {x x ≥ 1 , x ≠ 9 } B) {x x is any real number} C) {x x ≠ 9 , x ≠ 1 } D) {x 9 < x ≤ 10 }
Use the composition property to determine whether or not the functions are inverses of each other.
- f(x) = (x - 4)^2 , x ≥ 4; g(x) = x + 4 A) Yes B) No
Find the inverse of the given function f.
- f(x) = x^2 - 8
A) Not a one-to-one function B) f-^1 (x) (^) = x (^) + 8 C) f-^1 (x) (^) = x^2 + 8 D) f-^1 (x) (^) = x^2 - 8
If the following defines a one-to-one function, find the inverse.
- f(x) = (x + 2)^3 - 8.
A) f-1(x) =
x + 6 B) f-1(x) =
x + 10
C) f-1(x) =
x - 2 + 8 D) f-1(x) =
x + 8 - 2
The graph of a one-to-one function is given. Draw the graph of the inverse function f-^1. For convenience, the graph of y = x is also given.
Determine whether the given function is exponential of the fomr f(x) = ax^ or not. If it is exponential, identify the value of the base a.
x H(x)
2 4 81
3 8 729
A) Exponential; a = 9 2
B) Exponential; a = 2 9
C) Exponential; a (^) = 2 D) Not exponential
Solve the problem.
- If 3-x^ = 1 4
, what does 9x equal?
A) 16 B) 4 C) - 16 D) 1
The graph of an exponential function is given. Match the graph to one of the following functions.
-10 -5^5 10 x
y 10
5
-10 -5^5 10 x
y 10
5
A) f(x) = 3 x^ B) f(x) = 3 - x^ C) f(x) = - 3 - x^ D) f(x) = - 3 x
Solve the problem.
- The function f(x) = 700(0.5)x/^70 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 50 years. Round to the nearest whole number.
A) 427 pounds B) 490 pounds C) 250 pounds D) 265 pounds
- The function D(h) = 7e-0.4h^ can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after 12 hours?
A) 850.57 mg B) 0.06 mg C) 4.16 mg D) 0.73 mg
Solve the equation.
- 4
(^5) - 3 x = 1 256
A) 641 B) - 3 C) 128 D) 3
- 2x^2 -^3 = 64 A) {3, - 3} B) {3} C) { 35 , - 35 } D) {6}
Change the exponential expression to an equivalent logarithm expression.
- 3 -
A) log (^) - 3271 = 3 B) log 3 - 3 = 271 C) log 3271 = - 3 D) log (^) 1/27 3 = - 3
Change the logarithmic expression to an equivalent expression involving an exponent.
- log (^) 1/ 5 125 = - 3
A) 125 1/^5 = 3 B) (^15)
-^3
= 125 C) 15
= 125 D) (-3)1/^5 = 125
Find the exact value of the logarithmic expression.
- log 4 4
A) 12 B) 1 C) 4 D) (^14)
Use a calculator to evaluate the expression. Round your answer to three decimal places
- log ln 3^9 +^ log^4
A) (^) - 1.587 B) (^) - 3.654 C) (^) - 0.359 D) 0.
Find the domain of the function.
- f(x) = ln (^) x 1
A) ( 5 , (^) ∞) B) (- 5 , (^) ∞) C) (-∞, 5)∪(5, (^) ∞) D) (0, (^) ∞)
Susan purchased a painting in the year 2000 for $ 7000. Assuming an exponential rate of inflation of 3.2% per year, how much will the painting be worth 5 years later? A) $9176.03 B) $8214.58 C) $4891.02 D) $7812.
How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t) (^) = 450e-0.157t, where t is the time in years? Round to the nearest hundredth year. A) 38.91 yr B) 70.65 yr C) 43.33 yr D) 4.41 yr
The logistic growth model P(t) = 1890 1 + 62e-0.329t^
represents the population of a bacterium in a culture tube
after t hours. What was the initial amount of bacteria in the population? A) 31 B) 35 C) 29 D) 30
- The logistic growth model P(t) = 260 1 + 31.5e-0.175t^
represents the population of a species introduced into a
new territory after t years. When will the population be 70?
A) 14.01 years B) 12.22 years C) 0.79 years D) 2.58 years
Verify that the values of the variables listed are solutions of the system of equations.
x + y + z = - 8 x (^) - y (^) + 2z (^) = - 1 4x + y + z = - 17 x = - 1, y = - 4, z = - 3 A) solution B) not a solution
Solve the problem.
- The Family Fine Arts Center charges $ 22 per adult and $ 11 per senior citizen for its performances. On a recent weekend evening when 530 people paid admission, the total receipts were $7931. How many who paid were senior citizens? A) 191 senior citizens B) 281 senior citizens C) 339 senior citizens D) 249 senior citizens
Solve the system of equations.
x + y + z = 2 x - y + 4z = 22 2x + y + z = 4
A) ( 4 , (^) - 4 , 2 ) B) ( 4 , 2 , (^) - 4 ) C) ( 2 , (^) - 4 , 4 ) D) inconsistent
Perform the row operation(s) on the given augmented matrix.
- (a) R 2 = - 4 r 1 + r 2 (b) R3 = - 2r1 + r (c) R3 = 5r2 + r
A)
B)
C)
D)
Find the value of the determinant.
A) - 95 B) 35 C) 95 D) - 55
- Given that
x 1 1 4 3 2
= 2. Solve for x.
A) 13
B) 11
C) 3
D) - 11
- Suppose a linear system of three equations in three variables generates the following determintants:
D = - 81, Dx= - 243, Dy= 216, and Dz= - 9
Use Cramer's Rule to find the solution to this system.
A) (3, - 8
) B) ( 1
, 9) C) (3, - 5, 9) D) (3, - 2
Find the indicated expression.
- Let A (^) = 1 3 2 5
and B (^) = 0 4
A)
B)
C)
D)
Answer Key
Testname: 1073 TEST 3 REVIEW F
1) D
2) B
3) A
4) C
5) A
6) A
7) C
8) C
9) D
10) B
11) A
12) D
13) A
14) B
15) A
16) B
17) A
18) B
19) D
20) A
21) C
22) B
23) A
24) A
25) A
26) B
27) C
28) A
29) C
30) C
31) D
32) B
33) C
34) B
35) D
36) D
37) A
38) B
39) C
40) C
41) A
42) A
43) A
44) A
45) B
46) B
47) D
48) C
