MDTP Algebra 3 — Questions and Answers
Question 1: Which equation represents a function with a slope of -2 and y-intercept of 4?
- y = 4x - 2
- y = -2x + 4 (Correct answer)
- y = 2x - 4
- y = -4x + 2
Correct answer: y = -2x + 4
Using y = mx + b with m = -2 and b = 4 gives y = -2x + 4.
Question 2: Simplify: (x³)⁴
- x⁷
- x¹² (Correct answer)
- x³⁴
- 4x³
Correct answer: x¹²
When raising a power to a power, multiply the exponents: 3 × 4 = 12, giving x¹².
Question 3: What is the solution set of x² - 5x + 6 = 0?
- {2, 3} (Correct answer)
- {-2, -3}
- {1, 6}
- {-1, -6}
Correct answer: {2, 3}
Factoring gives (x - 2)(x - 3) = 0, so x = 2 or x = 3.
Question 4: If g(x) = x - 3 and h(x) = 2x, what is h(g(5))?
- 4 (Correct answer)
- 7
- 10
- 13
Correct answer: 4
g(5) = 5 - 3 = 2, then h(2) = 2(2) = 4.
Question 5: What is the range of f(x) = x² + 1?
- All real numbers
- y ≥ 0
- y ≥ 1 (Correct answer)
- y > 1
Correct answer: y ≥ 1
Since x² ≥ 0 for all x, x² + 1 ≥ 1, so the range is y ≥ 1.
Question 6: Solve for x: (x/3) + 2 = 5
- x = 1
- x = 7
- x = 9 (Correct answer)
- x = 21
Correct answer: x = 9
Subtracting 2 from both sides gives x/3 = 3, then multiplying by 3 gives x = 9.
MDTP Algebra 3
Which equation represents a function with a slope of -2 and y-intercept of 4?