MPT College Algebra 3 — Questions and Answers
Question 1: What is the domain of f(x) = √(2x - 6)?
- x ≥ 3 (Correct answer)
- x > 3
- x ≥ 6
- All real numbers
Correct answer: x ≥ 3
The radicand must be ≥ 0: 2x - 6 ≥ 0 → x ≥ 3.
Question 2: Which equation represents a circle with center (2, -1) and radius 4?
- (x-2)² + (y+1)² = 16 (Correct answer)
- (x+2)² + (y-1)² = 16
- (x-2)² + (y+1)² = 4
- (x+2)² + (y-1)² = 4
Correct answer: (x-2)² + (y+1)² = 16
Standard form (x-h)² + (y-k)² = r² with h=2, k=-1, r=4 gives (x-2)² + (y+1)² = 16.
Question 3: Solve for x: log₃(x) = 4
- 81 (Correct answer)
- 12
- 64
- 27
Correct answer: 81
Converting from log form: x = 3⁴ = 81.
Question 4: Factor completely: 2x² + 7x + 3
- (2x + 1)(x + 3) (Correct answer)
- (2x + 3)(x + 1)
- (x + 3)(x + 1)
- (2x - 1)(x - 3)
Correct answer: (2x + 1)(x + 3)
Check: (2x + 1)(x + 3) = 2x² + 6x + x + 3 = 2x² + 7x + 3.
Question 5: If f(x) = 2x + 1 and g(x) = x², what is (f ∘ g)(3)?
- 19 (Correct answer)
- 49
- 7
- 13
Correct answer: 19
(f ∘ g)(3) = f(g(3)) = f(9) = 2(9) + 1 = 19.
Question 6: What is the sum of the arithmetic series 2 + 5 + 8 + ... + 29?
- 155 (Correct answer)
- 140
- 170
- 120
Correct answer: 155
There are (29-2)/3 + 1 = 10 terms; sum = 10(2+29)/2 = 5(31) = 155.
Question 7: Which value of x satisfies 4^x = 32?
- 5/2 (Correct answer)
- 2
- 8
- 3/2
Correct answer: 5/2
Rewrite as 2^(2x) = 2⁵, so 2x = 5 and x = 5/2.
MPT College Algebra 3
What is the domain of f(x) = √(2x - 6)?