Mth 100 Practice Problems Test 2. Sections 4.4 - 6.5
SHORT ANSWER. Write the word or phrase that best
completes each statement or answers the question.
Name:____________________________
4) x + 5 ≥ 2y or x ≤ 3
y
Section 4.4
Graph the linear inequality in two variables.
1) x - y < -6
10
5
y
10
-10
-5
5
10
x
5
-5
-10
-5
5
10
x
-10
-5
Section 4.5
Decide whether the relation is a function.
5) {(-8, 2), (-8, 8), (1, -5), (4, -6), (8, -2)}
-10
2) x - 6y ≥ 0
6) {(-6, -1), (-2, -9), (3, 9), (6, -1)}
y
10
Give the domain and range of the relation.
7) {(-7, 5), (-7, -4), (-2, 8), (-3, 7), (3, 4)}
5
-10
-5
5
10
Decide whether the relation is a function, and give the
domain and range.
8)
x
-5
y
10
-10
5
Graph the compound inequality.
3) 2x - y > 4 and x ≤ 4
-10
y
-10
2
-2
5
-5
4
-4
-5
2
4
6x
-2
-4
-6
1
10
x
9)
Solve the system by elimination. If the system is
inconsistent or has dependent equations, say so.
18) x + 8y = 2
4x + 9y = 8
y
10
5
19) 9x + 37 = 8y
-4x + 5y = 15
-10
-5
5
10
x
20) 4x + 6y = 1
-12x - 18y = -3
-5
-10
21) 3x - 2y = 4
6x - 4y = -8
Determine whether the relation defines y as a function of
x. Give the domain.
10) y2 = 2x
Section 6.1
Apply the product rule for exponents, if possible.
22) 5 5 · 5 7
11) y = 4x - 2
12) y = 23) (-3x5 y)(-4x9 y2 )
3
x + 19
Evaluate the expression. Assume all variables represent
nonzero numbers.
24) -5 0
Solve the problem.
13) Find f(2) when f(x) = 4x2 + 5x + 2.
25) (-6)0
14) Find g(a - 1) when g(x) = 2x - 5.
Evaluate the expression.
1
26)
-7 -3
15) Find f(0) when
y
10
27)
5
-10
-5
5
y = f (x)
10
5 -4
4
Write the expression with only positive exponents.
Assume all variables represent nonzero numbers.
Simplify if necessary.
28) (-3)-4
x
-5
-10
29) (3p) -2
Section 5.1
Solve the system by substitution.
16) 3x - 13 = -y
2x + 9y = -8
30) 4x -4
17) 5x + y = 0
-5x + y = -10
2
Section 6.5
Divide.
Apply the quotient rule for exponents, if applicable, and
write the result using only positive exponents. Assume all
variables represent nonzero numbers.
x-12
31)
x-6
4
32)
4 -1
46)
16st4 - 5t6 + 64st3
4st3
48)
34) (-2x6 )3
Simplify the expression so that no negative exponents
appear in the final result. Assume all variables represent
nonzero numbers.
35) 7 6 7 -9
37)
35x7 - 42x6 + 35x5
7x6
47) ( 6 r3 - 41 r2 - 52 r - 32 ) ÷ (r - 8 )
Simplify the expression. Write your answer with only
positive exponents. Assume that all variables represent
nonzero real numbers.
7 2
33)
4
36)
45)
2x3 y-3 -5
x-2 y4
19r5 (r5 )2
7(r4 )-1
Section 6.4
Find the product.
38) (-4m 3 )(5m 2 )
39) (x2 + 9x - 5)(3x2 )
40) (x + 5)(x2 - x + 8)
41) (-4x - 4)(-5x - 2)
42) (2x2 - 9y)(2x2 + 9y)
43) (7m + 12)2
44) (4a - 3)2
3
x4 + 3x2 + 10
x2 + 1
Answer Key
Testname: 100 PRACTICE PROBLEMS TEST 2 S4.4 ‐ 6.5
1)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
2)
y
10
5
-10
-5
-5
-10
3)
y
4
2
-4
-2
2
4
6x
-2
-4
-6
4
Answer Key
Testname: 100 PRACTICE PROBLEMS TEST 2 S4.4 ‐ 6.5
4)
y
10
5
-10
-5
5
10
x
-5
-10
5) Not a function
6) Function
7) Domain: {-7, -2, 3, -3}; Range: {-4, 8, 4, 7, 5}
8) Not a function; domain: (-∞, 2] ; range: (-∞, ∞)
9) Function; domain: (-∞, ∞); range: (0, ∞)
10) Not a function; domain: [0, ∞)
1
11) Function; domain: , ∞
2
12) Function; domain: (-∞, -19) ∪ (-19, ∞)
13) 28
14) 2a - 7
15) -4
16) {(5, -2)}
17) {(1, -5)}
18) {(2, 0)}
19) {(-5, -1)}
20) Dependent: {(x, y) 4x + 6y = 1}
21) Inconsistent: no solutions
22) 5 12
23) 12x14y3
24) -1
25) 1
26) -343
256
27)
625
28)
29)
30)
31)
1
81
1
9p2
4
x4
1
x6
32) 4 2
5
Answer Key
Testname: 100 PRACTICE PROBLEMS TEST 2 S4.4 ‐ 6.5
33)
49
16
34) -8x18
1
35)
343
36)
y35
32x25
37)
19r19
7
38) -20m 5
39) 3x4 + 27x3 - 15x2
40) x3 + 4x2 + 3x + 40
41) 20x2 + 28x + 8
42) 4x4 - 81y2
43) 49m 2 + 168m + 144
44) 16a 2 - 24a + 9
5
45) 5x - 6 + x
46) 4t - 5t3
+ 16
4s
47) 6 r2 + 7 r + 4
8
48) x2 + 2 + 2
x + 1
6