Download MTH 112 test 4 practice problems spring 2014.tst

MTH 112 Test 4 Practice Problems
Spring 2014
For the given functions f and g , find the indicated
composition.
1) f(x) = 12x2 - 9x, g(x) = 18x - 3
Identify the intervals where the function is changing as
requested.
9) Constant, increasing, or decreasing
(f∘g)(8)
5
y
4
2) f(x) = -4x + 3,
(g∘f)(x)
3) f(x) =
g(x) = 6x + 4
3
2
1
x - 10
,
3
g(x) = 3x + 10
-5
-4
-3
-2
-1
1
2
3
4
5 x
-1
(g∘f)(x)
-2
4) f(x) = 4x2 + 6x + 4,
(g∘f)(x)
-3
g(x) = 6x - 5
-4
-5
Identify the intercepts.
5)
Use the graph of the given function to find any relative
maxima and relative minima.
10) f(x) = x3 - 3x2 + 1
y
10
5
5
y
4
3
-10
-5
5
10
x
2
1
-5
-5
-4
-3
-2
-1
1
-1
-10
-2
-3
Find and simplify the difference quotient
f(x + h) - f(x)
, h≠ 0 for the given function.
h
-4
-5
6) f(x) = x2 + 9x - 8
7) f(x) =3x2 - 5x - 4
8) f(x) =
1
6x
1
2
3
4
5 x
11) f(x) = x3 - 12x + 2
20
20) h(x) =
y
25x3
5x2 + 1
16
Find the slant asymptote, if any, of the graph of the
rational function.
x2 + 6x - 8
21) f(x) =
x-7
12
8
4
-5
-4
-3
-2
-1
1
2
3
4
5 x
-4
-8
22) f(x) =
x2 - 8x + 8
x+8
23) f(x) =
6x2
5x2 + 3
-12
-16
-20
Find the domain of the rational function. Write your
answer using interval notation.
x+4
12) f(x) =
x2 - 25
13) h(x) =
Find the center and the radius of the circle.
24) (x + 7)2 + (y + 8)2 = 49
Write the standard form of the equation of the circle with
the given center and radius.
25) (7, 8); 9
3x + 5
x2 - 2x -3
26) (0, 3);
Find the vertical asymptotes, if any, of the graph of the
rational function.
x
14) f(x) =
x2 + 4
15) h(x) =
16)
2
Complete the square and write the equation in standard
form. Then give the center and radius of the circle.
27) x2 + y2 - 4x + 16y + 68 = 9
x+2
x(x + 5)
Graph the equation. Give the domain and the radius.
28) x2 + y2 - 4x - 6y + 9 = 0
x - 25
2
x - 8x + 15
10
y
5
x+3
17) h(x) =
x2 - 9
-10
5
10 x
-5
Find the horizontal asymptote, if any, of the graph of the
rational function.
6x2
18) g(x) =
2x2 + 1
19) f(x) =
-5
-10
Solve the system by the substitution method.
29) 15x - y = 58
y = x2 - 2
15x
3x2 + 1
2
30) x + y = 6
y = x2 - 12x + 36
37) x2 + y2 ≤ 16
10
31) xy = 72
x + y = -17
y
5
Solve the system by the addition method.
32) x2 + y2 = 9
-10
-5
5
10 x
5
10 x
5
10 x
-5
x2 - y2 = 9
-10
33) x2 + y2 = 25
25x2 + 16y2 = 400
38) x2 + y2 > 49
34) x2 + y2 - 8x - 8y + 31 = 0
x2 - y2 - 8x + 8y - 1 = 0
10
y
5
Graph the inequality.
35) x - y > -4
-10
-5
y
10
-5
-10
-10
10
39) y ≤ x2 + 7
x
10
5
-10
-10
36) x > -5
-5
-5
y
10
-10
5
-10
-5
y
5
10
x
-5
-10
3
40) (x - 5)2 + (y - 4)2 > 4
43) x2 + y2 ≤ 49
7x + 5y ≤ 35
y
10
y
10
5
5
-10
-5
5
10
x
-10
-5
5
10
x
-5
-5
-10
-10
Graph the solution set of the system of inequalities or
indicate that the system has no solution.
41) 3x - y ≤ -3
x + 4y ≥ -4
44) x2 + y2 ≤ 64
x2 + y2 ≥ 49
y
y
10
6
8
4
6
2
4
2
-8
-6
-4
-2
2
4
6
8x
-2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-4
-4
-6
-6
-8
-10
45) x2 + y2 ≤ 25
y - x2 > 0
42) -1 ≤ y < 4
y
y
10
10
8
6
5
4
2
-10 -8 -6 -4 -2-2
2
4
6 8 10
-10
x
-5
5
10
x
-5
-4
-6
-8
-10
-10
Write the augmented matrix for the system of equations.
46) -2x + 5y + 9z = 52
3x + 9y + 8z = 97
8x + 6y + 8z = 88
4
47)
6x + 6z = 90
4y + 7z = 88
4x + 3y + 2z = 68
Write the system of linear equations represented by the
augmented matrix. Use x, y, z, and, if necessary, w for the
variables.
48)
2 6 4 -2
6 0 3 4
8 5 0 2
49)
8
-1
5
0
1
7
0
4
0 9
5
1 0 -10
0 3
9
0 -4 -7
Solve the system of equations using matrices. Use
Gaussian elimination with back-substitution.
50)
x + y + z = -1
x - y + 5z = 5
5x + y + z = 19
51)
x - y + 3z = -2
5x + z = 1
x + 4y + z = 21
Use Gaussian elimination to find the complete solution to
the system of equations, or state that none exists.
52) 5x + 2y + z = -11
2x - 3y - z = 17
7x - y = 12
53)
54)
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
x+ y+z = 9
2x - 3y + 4z = 7
x - 4y + 3z = -2
5
Answer Key
Testname: MTH 112 TEST 4 PRACTICE PROBLEMS SPRING 2014
1) 237,303
2) -24x + 22
3) x
4) 24x2 + 36x + 19
33) {(0, 5), (0, -5)}
34) {(5, 4), (3, 4)}
35)
y
10
5) x-intercepts:(6, 0), (-6, 0),
y-intercepts: (0, 7), (0, -7)
6) 2x + h + 9
7) 6x +3 h - 5
-1
8)
6x (x + h)
-10
9) constant: (-1, 1)
increasing: (-2, -1) ∪ (3, ∞)
decreasing: (1, 3)
10) maximum: (0, 1); minimum: (2, -3)
11) minimum: (2, -14); maximum: (-2, 18)
12) (-∞, -5) ∪ (-5, 5) ∪ (5, ∞)
13) (-∞, -1) ∪ (-1, 3) ∪ (3, ∞)
14) no vertical asymptote
15) x = 0 and x = -5
16) x = 5, x = 3
17) x = 3
18) y = 3
19) y = 0
20) no horizontal asymptote
21) y = x + 13
22) y = x - 16
23) no slant asymptote
24) (-7, -8), r = 7
25) (x - 7)2 + (y - 8)2 = 81
10
x
10
x
-10
36)
y
10
5
-10
-5
5
-5
-10
37)
26) x2 + (y - 3)2 = 2
27) (x - 2)2 + (x + 8)2 = 9
10
(2, -8), r = 3
y
5
28)
10
y
-10
-5
5
-5
5
-10
-10
-5
5
10 x
-5
-10
domain:[0, 4] range: [1, 5]
29) {(8, 62), (7, 47)}
30) {(5, 1), (6, 0)}
31) {(-8, -9), (-9, -8)}
32) {(3, 0), (-3, 0)}
6
10 x
Answer Key
Testname: MTH 112 TEST 4 PRACTICE PROBLEMS SPRING 2014
38)
42)
y
10
y
12
10
8
6
5
4
2
-10
-5
10 x
5
-10 -8 -6 -4 -2-2
-5
-4
-10
-6
-8
2
4 6
8 10
x
10
x
-10
39)
-12
y
10
43)
y
10
5
5
-10
-5
10 x
5
-5
-10
-5
5
-5
-10
y
-10
10
44)
5
y
6
-10
-5
5
10
x
4
2
-5
-8
-6
-4
-2
2
-2
-10
40)
41)
-4
-6
y
10
8
6
4
2
-10 -8 -6 -4 -2
-2
2
4
6
8 10 x
-4
-6
-8
-10
7
4
6
8x
Answer Key
Testname: MTH 112 TEST 4 PRACTICE PROBLEMS SPRING 2014
y
10
5
-10
-5
5
10
x
-5
-10
45)
46)
-2 5 9 52
3 9 8 97
8 6 8 88
47)
6 0 6 90
0 4 7 88
4 3 2 68
48) 2x + 6y + 4z = -2
6x + 3z = 4
8x + 5y = 2
49)
8x + y + 9w = 5
-x + 7y + z = -10
5x + 3w = 9
4y - 4w = -7
50) {(5, -5, -1)}
51) {(0, 5, 1)}
52) ∅
53) ∅
54) infinitely many solutions
7z 34 2z 11
{(,
, z)}
+
+
5
5 5
5
8